Skip to content

Mathematics · Ch 18 — Differentiation

Derivatives of Trigonometric Functions

18.2.6

Derivatives of Trigonometric Functions

A reference table of all six trigonometric-function derivatives:

y=f(x)dy/dx=f′(x)sin⁡xcos⁡xcos⁡x−sin⁡xtan⁡xsec⁡2xcot⁡x−cosec2xsec⁡xsec⁡xtan⁡xcosec x−cosec xcot⁡x\begin{array}{ll}y=f(x) & dy/dx=f'(x)\\ \hline \sin x & \cos x\\ \cos x & -\sin x\\ \tan x & \sec^2x\\ \cot x & -\text{cosec}^2x\\ \sec x & \sec x\tan x\\ \text{cosec}\,x & -\text{cosec}\,x\cot x\end{array} …

Table 1Table 9.2.6 — trigonometric function derivatives

y = f(x) -> dy/dx = f'(x)

sin x -> cos x

cos x -> -sin x

tan x -> sec^2 x

cot x -> -cosec^2 x

sec x -> sec x tan x …