Derivatives of Trigonometric Functions
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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 $\sin x \ne 0$.