Worksheet · Calculus I · Unit 2A

Chain Rule Worksheet with Answers and Worked Solutions

Twenty-four composition problems from basic powers through nested, product, and quotient combinations.

24 problems60 min estimated timeFoundational to advanced progression

What is included

Build chain-rule fluency with a printable worksheet, complete key, error analysis, and worked HTML solutions.

Skills assessed

composition structure
nested chain rule
product plus chain
quotient plus chain

Prerequisites

basic derivative rules
function composition

Printable and accessible

Download this resource

No email address or account is required.

Student PDF Worked answer key PDF

Device-only study control

Ready for an honest first attempt?

This control sends only the resource id and type—never your answers or identity.

Printable preview

Differentiate $y=(3x+2)^{5}$ .
Differentiate $y=(5x-1)^{4}$ .
Differentiate $y=(2x+4)^{6}$ .
Differentiate $y=(-3x+2)^{3}$ .
Differentiate $y=(7x+1)^{2}$ .
Differentiate $y=(4x-5)^{3}$ .
Differentiate $y=e^{3x^2}$ .
Differentiate $y=e^{\sin x}$ .
Differentiate $y=\ln(5x-2)$ .
Differentiate $y=\ln(x^2+4)$ .
Differentiate $y=\sin(4x^3)$ .
Differentiate $y=\cos(2x-1)$ .
Differentiate $y=\tan(x^2)$ .
Differentiate $y=\sin^3 x$ .
Differentiate $y=(1+(2x-3)^2)^4$ .
Differentiate $y=e^{\sqrt{1+x^2}}$ .
Differentiate $y=\ln(1+\sin^2x)$ .
Differentiate $y=x^2e^{3x}$ .
Differentiate $y=x\sin(x^2)$ .
Differentiate $y=\frac{\ln x}{x^2}$ .
Differentiate $y=\frac{e^x}{1+x^2}$ .
Differentiate $y=(x^2+1)^3(x-2)$ .
Differentiate $y=\frac{\sin(2x)}{x}$ .
Differentiate $y=\sqrt{1+e^{2x}}$ .

Complete worked solutions

Every problem has a source-matched answer and independently reviewed derivation.

Problem 1: Differentiate $y=(3x+2)^{5}$ .

Answer: $y'=15(3x+2)^{4}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{5}$ .
Multiply by the inner derivative $3$ .

Problem 2: Differentiate $y=(5x-1)^{4}$ .

Answer: $y'=20(5x-1)^{3}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{4}$ .
Multiply by the inner derivative $5$ .

Problem 3: Differentiate $y=(2x+4)^{6}$ .

Answer: $y'=12(2x+4)^{5}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{6}$ .
Multiply by the inner derivative $2$ .

Problem 4: Differentiate $y=(-3x+2)^{3}$ .

Answer: $y'=-9(-3x+2)^{2}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{3}$ .
Multiply by the inner derivative $-3$ .

Problem 5: Differentiate $y=(7x+1)^{2}$ .

Answer: $y'=14(7x+1)^{1}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{2}$ .
Multiply by the inner derivative $7$ .

Problem 6: Differentiate $y=(4x-5)^{3}$ .

Answer: $y'=12(4x-5)^{2}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{3}$ .
Multiply by the inner derivative $4$ .

Problem 7: Differentiate $y=e^{3x^2}$ .

Answer: $y'=6xe^{3x^2}$

Why this method: Exponential or logarithmic chain rule matches the mathematical structure before any algebraic cleanup.

Treat $3x^2$ as the inner function.
Differentiate the outer function and multiply by $6x$ .

Problem 8: Differentiate $y=e^{\sin x}$ .

Answer: $y'=e^{\sin x}\cos x$

Why this method: Exponential or logarithmic chain rule matches the mathematical structure before any algebraic cleanup.

Treat $\sin x$ as the inner function.
Differentiate the outer function and multiply by $\cos x$ .

Problem 9: Differentiate $y=\ln(5x-2)$ .

Answer: $y'=\frac5{5x-2}$

Why this method: Exponential or logarithmic chain rule matches the mathematical structure before any algebraic cleanup.

Treat $5x-2$ as the inner function.
Differentiate the outer function and multiply by $5$ .

Problem 10: Differentiate $y=\ln(x^2+4)$ .

Answer: $y'=\frac{2x}{x^2+4}$

Why this method: Exponential or logarithmic chain rule matches the mathematical structure before any algebraic cleanup.

Treat $x^2+4$ as the inner function.
Differentiate the outer function and multiply by $2x$ .

Problem 11: Differentiate $y=\sin(4x^3)$ .

Answer: $y'=12x^2\cos(4x^3)$

Why this method: Trigonometric chain rule matches the mathematical structure before any algebraic cleanup.

Identify the outer trigonometric function and preserve its inner input.
Differentiate the inner expression and multiply.

Problem 12: Differentiate $y=\cos(2x-1)$ .

Answer: $y'=-2\sin(2x-1)$

Why this method: Trigonometric chain rule matches the mathematical structure before any algebraic cleanup.

Identify the outer trigonometric function and preserve its inner input.
Differentiate the inner expression and multiply.

Problem 13: Differentiate $y=\tan(x^2)$ .

Answer: $y'=2x\sec^2(x^2)$

Why this method: Trigonometric chain rule matches the mathematical structure before any algebraic cleanup.

Identify the outer trigonometric function and preserve its inner input.
Differentiate the inner expression and multiply.

Problem 14: Differentiate $y=\sin^3 x$ .

Answer: $y'=3\sin^2x\cos x$

Why this method: Trigonometric chain rule matches the mathematical structure before any algebraic cleanup.

Identify the outer trigonometric function and preserve its inner input.
Differentiate the inner expression and multiply.

Problem 15: Differentiate $y=(1+(2x-3)^2)^4$ .

Answer: $y'=16(2x-3)(1+(2x-3)^2)^3$

Why this method: Nested chain rule matches the mathematical structure before any algebraic cleanup.

Write the composition as nested layers from outside to inside.
Differentiate each layer once and multiply the factors.

Problem 16: Differentiate $y=e^{\sqrt{1+x^2}}$ .

Answer: $y'=\frac{x e^{\sqrt{1+x^2}}}{\sqrt{1+x^2}}$

Why this method: Nested chain rule matches the mathematical structure before any algebraic cleanup.

Write the composition as nested layers from outside to inside.
Differentiate each layer once and multiply the factors.

Problem 17: Differentiate $y=\ln(1+\sin^2x)$ .

Answer: $y'=\frac{2\sin x\cos x}{1+\sin^2x}$

Why this method: Nested chain rule matches the mathematical structure before any algebraic cleanup.

Write the composition as nested layers from outside to inside.
Differentiate each layer once and multiply the factors.

Problem 18: Differentiate $y=x^2e^{3x}$ .

Answer: $y'=e^{3x}(2x+3x^2)$

Why this method: product plus chain matches the mathematical structure before any algebraic cleanup.

Apply the product plus chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $e^{3x}(2x+3x^2)$ .

Problem 19: Differentiate $y=x\sin(x^2)$ .

Answer: $y'=\sin(x^2)+2x^2\cos(x^2)$

Why this method: product plus chain matches the mathematical structure before any algebraic cleanup.

Apply the product plus chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $\sin(x^2)+2x^2\cos(x^2)$ .

Problem 20: Differentiate $y=\frac{\ln x}{x^2}$ .

Answer: $y'=\frac{1-2\ln x}{x^3}$

Why this method: quotient plus chain matches the mathematical structure before any algebraic cleanup.

Apply the quotient plus chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $\frac{1-2\ln x}{x^3}$ .

Problem 21: Differentiate $y=\frac{e^x}{1+x^2}$ .

Answer: $y'=\frac{e^x(1+x^2-2x)}{(1+x^2)^2}$

Why this method: quotient rule matches the mathematical structure before any algebraic cleanup.

Apply the quotient rule structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $\frac{e^x(1+x^2-2x)}{(1+x^2)^2}$ .

Problem 22: Differentiate $y=(x^2+1)^3(x-2)$ .

Answer: $y'=(x^2+1)^2(7x^2-12x+1)$

Why this method: product plus chain matches the mathematical structure before any algebraic cleanup.

Apply the product plus chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $(x^2+1)^2(7x^2-12x+1)$ .

Problem 23: Differentiate $y=\frac{\sin(2x)}{x}$ .

Answer: $y'=\frac{2x\cos(2x)-\sin(2x)}{x^2}$

Why this method: quotient plus chain matches the mathematical structure before any algebraic cleanup.

Apply the quotient plus chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $\frac{2x\cos(2x)-\sin(2x)}{x^2}$ .

Problem 24: Differentiate $y=\sqrt{1+e^{2x}}$ .

Answer: $y'=\frac{e^{2x}}{\sqrt{1+e^{2x}}}$

Why this method: nested chain matches the mathematical structure before any algebraic cleanup.

Apply the nested chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $\frac{e^{2x}}{\sqrt{1+e^{2x}}}$ .

Common errors

Forgetting an inner derivative.
Applying the chain rule to a sum or product as a single composition.
Simplifying before the rule structure is secure.

Worksheet · Calculus I · Unit 2A

Chain Rule Worksheet with Answers and Worked Solutions

Twenty-four composition problems from basic powers through nested, product, and quotient combinations.

24 problems60 min estimated timeFoundational to advanced progression

What is included

Build chain-rule fluency with a printable worksheet, complete key, error analysis, and worked HTML solutions.

Skills assessed

composition structure
nested chain rule
product plus chain
quotient plus chain

Prerequisites

basic derivative rules
function composition

Printable and accessible

Download this resource

No email address or account is required.

Student PDF Worked answer key PDF

Device-only study control

Ready for an honest first attempt?

This control sends only the resource id and type—never your answers or identity.

Printable preview

Differentiate $y=(3x+2)^{5}$ .
Differentiate $y=(5x-1)^{4}$ .
Differentiate $y=(2x+4)^{6}$ .
Differentiate $y=(-3x+2)^{3}$ .
Differentiate $y=(7x+1)^{2}$ .
Differentiate $y=(4x-5)^{3}$ .
Differentiate $y=e^{3x^2}$ .
Differentiate $y=e^{\sin x}$ .
Differentiate $y=\ln(5x-2)$ .
Differentiate $y=\ln(x^2+4)$ .
Differentiate $y=\sin(4x^3)$ .
Differentiate $y=\cos(2x-1)$ .
Differentiate $y=\tan(x^2)$ .
Differentiate $y=\sin^3 x$ .
Differentiate $y=(1+(2x-3)^2)^4$ .
Differentiate $y=e^{\sqrt{1+x^2}}$ .
Differentiate $y=\ln(1+\sin^2x)$ .
Differentiate $y=x^2e^{3x}$ .
Differentiate $y=x\sin(x^2)$ .
Differentiate $y=\frac{\ln x}{x^2}$ .
Differentiate $y=\frac{e^x}{1+x^2}$ .
Differentiate $y=(x^2+1)^3(x-2)$ .
Differentiate $y=\frac{\sin(2x)}{x}$ .
Differentiate $y=\sqrt{1+e^{2x}}$ .

Complete worked solutions

Every problem has a source-matched answer and independently reviewed derivation.

Problem 1: Differentiate $y=(3x+2)^{5}$ .

Answer: $y'=15(3x+2)^{4}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{5}$ .
Multiply by the inner derivative $3$ .

Problem 2: Differentiate $y=(5x-1)^{4}$ .

Answer: $y'=20(5x-1)^{3}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{4}$ .
Multiply by the inner derivative $5$ .

Problem 3: Differentiate $y=(2x+4)^{6}$ .

Answer: $y'=12(2x+4)^{5}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{6}$ .
Multiply by the inner derivative $2$ .

Problem 4: Differentiate $y=(-3x+2)^{3}$ .

Answer: $y'=-9(-3x+2)^{2}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{3}$ .
Multiply by the inner derivative $-3$ .

Problem 5: Differentiate $y=(7x+1)^{2}$ .

Answer: $y'=14(7x+1)^{1}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{2}$ .
Multiply by the inner derivative $7$ .

Problem 6: Differentiate $y=(4x-5)^{3}$ .

Answer: $y'=12(4x-5)^{2}$

Why this method: Basic chain rule matches the mathematical structure before any algebraic cleanup.

Use the power rule on the outer power $u^{3}$ .
Multiply by the inner derivative $4$ .

Problem 7: Differentiate $y=e^{3x^2}$ .

Answer: $y'=6xe^{3x^2}$

Why this method: Exponential or logarithmic chain rule matches the mathematical structure before any algebraic cleanup.

Treat $3x^2$ as the inner function.
Differentiate the outer function and multiply by $6x$ .

Problem 8: Differentiate $y=e^{\sin x}$ .

Answer: $y'=e^{\sin x}\cos x$

Why this method: Exponential or logarithmic chain rule matches the mathematical structure before any algebraic cleanup.

Treat $\sin x$ as the inner function.
Differentiate the outer function and multiply by $\cos x$ .

Problem 9: Differentiate $y=\ln(5x-2)$ .

Answer: $y'=\frac5{5x-2}$

Why this method: Exponential or logarithmic chain rule matches the mathematical structure before any algebraic cleanup.

Treat $5x-2$ as the inner function.
Differentiate the outer function and multiply by $5$ .

Problem 10: Differentiate $y=\ln(x^2+4)$ .

Answer: $y'=\frac{2x}{x^2+4}$

Why this method: Exponential or logarithmic chain rule matches the mathematical structure before any algebraic cleanup.

Treat $x^2+4$ as the inner function.
Differentiate the outer function and multiply by $2x$ .

Problem 11: Differentiate $y=\sin(4x^3)$ .

Answer: $y'=12x^2\cos(4x^3)$

Why this method: Trigonometric chain rule matches the mathematical structure before any algebraic cleanup.

Identify the outer trigonometric function and preserve its inner input.
Differentiate the inner expression and multiply.

Problem 12: Differentiate $y=\cos(2x-1)$ .

Answer: $y'=-2\sin(2x-1)$

Why this method: Trigonometric chain rule matches the mathematical structure before any algebraic cleanup.

Identify the outer trigonometric function and preserve its inner input.
Differentiate the inner expression and multiply.

Problem 13: Differentiate $y=\tan(x^2)$ .

Answer: $y'=2x\sec^2(x^2)$

Why this method: Trigonometric chain rule matches the mathematical structure before any algebraic cleanup.

Identify the outer trigonometric function and preserve its inner input.
Differentiate the inner expression and multiply.

Problem 14: Differentiate $y=\sin^3 x$ .

Answer: $y'=3\sin^2x\cos x$

Why this method: Trigonometric chain rule matches the mathematical structure before any algebraic cleanup.

Identify the outer trigonometric function and preserve its inner input.
Differentiate the inner expression and multiply.

Problem 15: Differentiate $y=(1+(2x-3)^2)^4$ .

Answer: $y'=16(2x-3)(1+(2x-3)^2)^3$

Why this method: Nested chain rule matches the mathematical structure before any algebraic cleanup.

Write the composition as nested layers from outside to inside.
Differentiate each layer once and multiply the factors.

Problem 16: Differentiate $y=e^{\sqrt{1+x^2}}$ .

Answer: $y'=\frac{x e^{\sqrt{1+x^2}}}{\sqrt{1+x^2}}$

Why this method: Nested chain rule matches the mathematical structure before any algebraic cleanup.

Write the composition as nested layers from outside to inside.
Differentiate each layer once and multiply the factors.

Problem 17: Differentiate $y=\ln(1+\sin^2x)$ .

Answer: $y'=\frac{2\sin x\cos x}{1+\sin^2x}$

Why this method: Nested chain rule matches the mathematical structure before any algebraic cleanup.

Write the composition as nested layers from outside to inside.
Differentiate each layer once and multiply the factors.

Problem 18: Differentiate $y=x^2e^{3x}$ .

Answer: $y'=e^{3x}(2x+3x^2)$

Why this method: product plus chain matches the mathematical structure before any algebraic cleanup.

Apply the product plus chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $e^{3x}(2x+3x^2)$ .

Problem 19: Differentiate $y=x\sin(x^2)$ .

Answer: $y'=\sin(x^2)+2x^2\cos(x^2)$

Why this method: product plus chain matches the mathematical structure before any algebraic cleanup.

Apply the product plus chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $\sin(x^2)+2x^2\cos(x^2)$ .

Problem 20: Differentiate $y=\frac{\ln x}{x^2}$ .

Answer: $y'=\frac{1-2\ln x}{x^3}$

Why this method: quotient plus chain matches the mathematical structure before any algebraic cleanup.

Apply the quotient plus chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $\frac{1-2\ln x}{x^3}$ .

Problem 21: Differentiate $y=\frac{e^x}{1+x^2}$ .

Answer: $y'=\frac{e^x(1+x^2-2x)}{(1+x^2)^2}$

Why this method: quotient rule matches the mathematical structure before any algebraic cleanup.

Apply the quotient rule structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $\frac{e^x(1+x^2-2x)}{(1+x^2)^2}$ .

Problem 22: Differentiate $y=(x^2+1)^3(x-2)$ .

Answer: $y'=(x^2+1)^2(7x^2-12x+1)$

Why this method: product plus chain matches the mathematical structure before any algebraic cleanup.

Apply the product plus chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $(x^2+1)^2(7x^2-12x+1)$ .

Problem 23: Differentiate $y=\frac{\sin(2x)}{x}$ .

Answer: $y'=\frac{2x\cos(2x)-\sin(2x)}{x^2}$

Why this method: quotient plus chain matches the mathematical structure before any algebraic cleanup.

Apply the quotient plus chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $\frac{2x\cos(2x)-\sin(2x)}{x^2}$ .

Problem 24: Differentiate $y=\sqrt{1+e^{2x}}$ .

Answer: $y'=\frac{e^{2x}}{\sqrt{1+e^{2x}}}$

Why this method: nested chain matches the mathematical structure before any algebraic cleanup.

Apply the nested chain structure before simplifying.
Retain every factor contributed by an inner derivative.
A factored final form is $\frac{e^{2x}}{\sqrt{1+e^{2x}}}$ .

Common errors

Forgetting an inner derivative.
Applying the chain rule to a sum or product as a single composition.
Simplifying before the rule structure is secure.

What is included

Skills assessed

Prerequisites

Download this resource

Ready for an honest first attempt?

Printable preview

Complete worked solutions

Problem 1: Differentiate y=(3x+2)5y=(3x+2)^{5}y=(3x+2)5.

Problem 2: Differentiate y=(5x−1)4y=(5x-1)^{4}y=(5x−1)4.

Problem 3: Differentiate y=(2x+4)6y=(2x+4)^{6}y=(2x+4)6.

Problem 4: Differentiate y=(−3x+2)3y=(-3x+2)^{3}y=(−3x+2)3.

Problem 5: Differentiate y=(7x+1)2y=(7x+1)^{2}y=(7x+1)2.

Problem 6: Differentiate y=(4x−5)3y=(4x-5)^{3}y=(4x−5)3.

Problem 7: Differentiate y=e3x2y=e^{3x^2}y=e3x2.

Problem 8: Differentiate y=esin⁡xy=e^{\sin x}y=esinx.

Problem 9: Differentiate y=ln⁡(5x−2)y=\ln(5x-2)y=ln(5x−2).

Problem 10: Differentiate y=ln⁡(x2+4)y=\ln(x^2+4)y=ln(x2+4).

Problem 11: Differentiate y=sin⁡(4x3)y=\sin(4x^3)y=sin(4x3).

Problem 12: Differentiate y=cos⁡(2x−1)y=\cos(2x-1)y=cos(2x−1).

Problem 13: Differentiate y=tan⁡(x2)y=\tan(x^2)y=tan(x2).

Problem 14: Differentiate y=sin⁡3xy=\sin^3 xy=sin3x.

Problem 15: Differentiate y=(1+(2x−3)2)4y=(1+(2x-3)^2)^4y=(1+(2x−3)2)4.

Problem 16: Differentiate y=e1+x2y=e^{\sqrt{1+x^2}}y=e1+x2​.

Problem 17: Differentiate y=ln⁡(1+sin⁡2x)y=\ln(1+\sin^2x)y=ln(1+sin2x).

Problem 18: Differentiate y=x2e3xy=x^2e^{3x}y=x2e3x.

Problem 19: Differentiate y=xsin⁡(x2)y=x\sin(x^2)y=xsin(x2).

Problem 20: Differentiate y=ln⁡xx2y=\frac{\ln x}{x^2}y=x2lnx​.

Problem 21: Differentiate y=ex1+x2y=\frac{e^x}{1+x^2}y=1+x2ex​.

Problem 22: Differentiate y=(x2+1)3(x−2)y=(x^2+1)^3(x-2)y=(x2+1)3(x−2).

Problem 23: Differentiate y=sin⁡(2x)xy=\frac{\sin(2x)}{x}y=xsin(2x)​.

Problem 24: Differentiate y=1+e2xy=\sqrt{1+e^{2x}}y=1+e2x​.

Common errors

Continue learning

Lessons and articles

Related resources

Glossary

What is included

Skills assessed

Prerequisites

Download this resource

Ready for an honest first attempt?

Printable preview

Complete worked solutions

Problem 1: Differentiate y=(3x+2)5y=(3x+2)^{5}y=(3x+2)5.

Problem 2: Differentiate y=(5x−1)4y=(5x-1)^{4}y=(5x−1)4.

Problem 3: Differentiate y=(2x+4)6y=(2x+4)^{6}y=(2x+4)6.

Problem 4: Differentiate y=(−3x+2)3y=(-3x+2)^{3}y=(−3x+2)3.

Problem 5: Differentiate y=(7x+1)2y=(7x+1)^{2}y=(7x+1)2.

Problem 6: Differentiate y=(4x−5)3y=(4x-5)^{3}y=(4x−5)3.

Problem 7: Differentiate y=e3x2y=e^{3x^2}y=e3x2.

Problem 8: Differentiate y=esin⁡xy=e^{\sin x}y=esinx.

Problem 9: Differentiate y=ln⁡(5x−2)y=\ln(5x-2)y=ln(5x−2).

Problem 10: Differentiate y=ln⁡(x2+4)y=\ln(x^2+4)y=ln(x2+4).

Problem 11: Differentiate y=sin⁡(4x3)y=\sin(4x^3)y=sin(4x3).

Problem 12: Differentiate y=cos⁡(2x−1)y=\cos(2x-1)y=cos(2x−1).

Problem 13: Differentiate y=tan⁡(x2)y=\tan(x^2)y=tan(x2).

Problem 14: Differentiate y=sin⁡3xy=\sin^3 xy=sin3x.

Problem 15: Differentiate y=(1+(2x−3)2)4y=(1+(2x-3)^2)^4y=(1+(2x−3)2)4.

Problem 16: Differentiate y=e1+x2y=e^{\sqrt{1+x^2}}y=e1+x2​.

Problem 17: Differentiate y=ln⁡(1+sin⁡2x)y=\ln(1+\sin^2x)y=ln(1+sin2x).

Problem 18: Differentiate y=x2e3xy=x^2e^{3x}y=x2e3x.

Problem 19: Differentiate y=xsin⁡(x2)y=x\sin(x^2)y=xsin(x2).

Problem 20: Differentiate y=ln⁡xx2y=\frac{\ln x}{x^2}y=x2lnx​.

Problem 21: Differentiate y=ex1+x2y=\frac{e^x}{1+x^2}y=1+x2ex​.

Problem 22: Differentiate y=(x2+1)3(x−2)y=(x^2+1)^3(x-2)y=(x2+1)3(x−2).

Problem 23: Differentiate y=sin⁡(2x)xy=\frac{\sin(2x)}{x}y=xsin(2x)​.

Problem 24: Differentiate y=1+e2xy=\sqrt{1+e^{2x}}y=1+e2x​.

Common errors

Continue learning

Lessons and articles

Related resources

Glossary

Problem 1: Differentiate $y=(3x+2)^{5}$ .

Problem 2: Differentiate $y=(5x-1)^{4}$ .

Problem 3: Differentiate $y=(2x+4)^{6}$ .

Problem 4: Differentiate $y=(-3x+2)^{3}$ .

Problem 5: Differentiate $y=(7x+1)^{2}$ .

Problem 6: Differentiate $y=(4x-5)^{3}$ .

Problem 7: Differentiate $y=e^{3x^2}$ .

Problem 8: Differentiate $y=e^{\sin x}$ .

Problem 9: Differentiate $y=\ln(5x-2)$ .

Problem 10: Differentiate $y=\ln(x^2+4)$ .

Problem 11: Differentiate $y=\sin(4x^3)$ .

Problem 12: Differentiate $y=\cos(2x-1)$ .

Problem 13: Differentiate $y=\tan(x^2)$ .

Problem 14: Differentiate $y=\sin^3 x$ .

Problem 15: Differentiate $y=(1+(2x-3)^2)^4$ .

Problem 16: Differentiate $y=e^{\sqrt{1+x^2}}$ .

Problem 17: Differentiate $y=\ln(1+\sin^2x)$ .

Problem 18: Differentiate $y=x^2e^{3x}$ .

Problem 19: Differentiate $y=x\sin(x^2)$ .

Problem 20: Differentiate $y=\frac{\ln x}{x^2}$ .

Problem 21: Differentiate $y=\frac{e^x}{1+x^2}$ .

Problem 22: Differentiate $y=(x^2+1)^3(x-2)$ .

Problem 23: Differentiate $y=\frac{\sin(2x)}{x}$ .

Problem 24: Differentiate $y=\sqrt{1+e^{2x}}$ .

Problem 1: Differentiate $y=(3x+2)^{5}$ .

Problem 2: Differentiate $y=(5x-1)^{4}$ .

Problem 3: Differentiate $y=(2x+4)^{6}$ .

Problem 4: Differentiate $y=(-3x+2)^{3}$ .

Problem 5: Differentiate $y=(7x+1)^{2}$ .

Problem 6: Differentiate $y=(4x-5)^{3}$ .

Problem 7: Differentiate $y=e^{3x^2}$ .

Problem 8: Differentiate $y=e^{\sin x}$ .

Problem 9: Differentiate $y=\ln(5x-2)$ .

Problem 10: Differentiate $y=\ln(x^2+4)$ .

Problem 11: Differentiate $y=\sin(4x^3)$ .

Problem 12: Differentiate $y=\cos(2x-1)$ .

Problem 13: Differentiate $y=\tan(x^2)$ .

Problem 14: Differentiate $y=\sin^3 x$ .

Problem 15: Differentiate $y=(1+(2x-3)^2)^4$ .

Problem 16: Differentiate $y=e^{\sqrt{1+x^2}}$ .

Problem 17: Differentiate $y=\ln(1+\sin^2x)$ .

Problem 18: Differentiate $y=x^2e^{3x}$ .

Problem 19: Differentiate $y=x\sin(x^2)$ .

Problem 20: Differentiate $y=\frac{\ln x}{x^2}$ .

Problem 21: Differentiate $y=\frac{e^x}{1+x^2}$ .

Problem 22: Differentiate $y=(x^2+1)^3(x-2)$ .

Problem 23: Differentiate $y=\frac{\sin(2x)}{x}$ .

Problem 24: Differentiate $y=\sqrt{1+e^{2x}}$ .