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Trigonometric derivatives

This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.

Trigonometric derivatives

Derivatives of trigonometric functions

$\frac{d}{d x} \sin x = \cos x$ $\frac{d}{d x} \cos x = - \sin x$

$\frac{d}{d x} \tan x = \sec^{2} x$ $\frac{d}{d x} \csc x = - \csc x \cot x$

$\frac{d}{d x} \sec x = \sec x \tan x$ $\frac{d}{d x} \cot x = - \csc^{2} x$

Index

Chapter 3 - Special Derivatives

Chapter 9 - Trigonometric Substitution

Glossary and deeper reading · 1 refreshers

These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.

Derivative
A derivative gives the instantaneous rate of change of a function with respect to its input. At a point, it is the finite limit of the difference quotient when that limit exists. For example, the derivative of x² is 2x, so the tangent slope at x=3 is 6. A derivative function collects those rates across the inputs where the function is differentiable.
Read more: 2.2 · Derivative →

Derivative

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