Derivatives of Trigonometric Functions

From ProofWiki
Jump to navigation Jump to search

Theorem

This page gathers together derivatives of trigonometric functions.


Derivative of Sine Function

$\map {\dfrac \d {\d x} } {\sin x} = \cos x$


Derivative of Cosine Function

$\map {\dfrac \d {\d x} } {\cos x} = -\sin x$


Derivative of Tangent Function

$\map {\dfrac \d {\d x} } {\tan x} = \sec^2 x = \dfrac 1 {\cos^2 x}$

when $\cos x \ne 0$.


Derivative of Cotangent Function

$\map {\dfrac \d {\d x} } {\cot x} = -\csc^2 x = \dfrac {-1} {\sin^2 x}$

where $\sin x \ne 0$.


Derivative of Secant Function

$\map {\dfrac \d {\d x} } {\sec x} = \sec x \tan x$

where $\cos x \ne 0$.


Derivative of Cosecant Function

$\map {\dfrac \d {\d x} } {\csc x} = -\csc x \cot x$

where $\sin x \ne 0$.