Common Derivative Computation Errors and How to Repair Them

Errors That Repeat Until They Are Named

• Evaluating $f(a+h)$ incompletely. Replace every occurrence of the input by the full expression $a+h$. • Cancelling terms instead of factors. Factor first; cancellation applies to common multiplicative factors. • Forgetting the chain factor. Audit every inner function after differentiating. • Using $(fg)'=f'g'$. The product rule has two terms. • Reversing the quotient-rule numerator. Use $f'g-fg'$ and keep the order consistent. • Dropping $y'$ in implicit differentiation. Every differentiated $y$-expression needs the chain rule. • Confusing inverse and reciprocal. $f^{-1}$ is the inverse function; $1/f$ is the reciprocal. • Using the power rule on $x^x$. The exponent is not constant; take logarithms. • Ignoring domains. Logarithms, roots, denominators, and inverse trig derivatives carry restrictions. • Expanding a useful factored result into debris. Simplification should reveal structure, not punish it.