Formula sheet · Calculus I · Unit 2A

Derivative Rules Formula Sheet and Printable PDF

A compact, readable reference for core derivative rules with rule-selection cues and examples.

Reference format15 min estimated timeReference progression

What is included

Review power, product, quotient, chain, exponential, logarithmic, trigonometric, and inverse-trigonometric derivative rules.

Skills assessed

selecting derivative rules
differentiating standard functions

Prerequisites

function notation
algebra

Derivative Rules Formula Sheet instructional sequence — A compact, readable reference for core derivative rules with rule-selection cues and examples. The numbered labels and written sequence preserve meaning without relying on color.

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Reference formulas

Linearity

(c)'=0

(x^n)'=nx^{n-1}

(f\pm g)'=f'\pm g'

Products and quotients

(fg)'=f'g+fg'

(f/g)'=(f'g-fg')/g^2

Composition

(f\circ g)'=f'(g(x))g'(x)

Exponential and logarithmic

(e^x)'=e^x

(a^x)'=a^x\ln a

(\ln x)'=1/x

Trigonometric

(\sin x)'=\cos x

(\cos x)'=-\sin x

(\tan x)'=\sec^2x

Inverse trigonometric

(\arcsin x)'=1/\sqrt{1-x^2}

(\arctan x)'=1/(1+x^2)

Common errors

Multiplying derivatives in a product.
Reversing quotient-rule numerator order.
Forgetting the inner derivative in a composition.

Reference formulas

Linearity

(c)'=0

(x^n)'=nx^{n-1}

(f\pm g)'=f'\pm g'

Products and quotients

(fg)'=f'g+fg'

(f/g)'=(f'g-fg')/g^2

Composition

(f\circ g)'=f'(g(x))g'(x)

Exponential and logarithmic

(e^x)'=e^x

(a^x)'=a^x\ln a

(\ln x)'=1/x

Trigonometric

(\sin x)'=\cos x

(\cos x)'=-\sin x

(\tan x)'=\sec^2x

Inverse trigonometric

(\arcsin x)'=1/\sqrt{1-x^2}

(\arctan x)'=1/(1+x^2)

What is included

Skills assessed

Prerequisites

Download this resource

Reference formulas

Linearity

Products and quotients

Composition

Exponential and logarithmic

Trigonometric

Inverse trigonometric

Common errors

Continue learning

Lessons and articles

Related resources

Glossary

What is included

Skills assessed

Prerequisites

Download this resource

Reference formulas

Linearity

Products and quotients

Composition

Exponential and logarithmic

Trigonometric

Inverse trigonometric

Common errors

Continue learning

Lessons and articles

Related resources

Glossary