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Derivatives of Trigonometric functions

There are six trigonometric functions in trigonometry. Each trigonometric function often involves in differential calculus. So, it is very important to learn the derivative of each trigonometric ratio. The following is the list of derivatives of trigonometric functions and they are used as formulas in differential calculus.

Differentiation of Sine function

The derivative of $\sin{x}$ with respect $x$ is equal to $cos{x}$.

$\large \dfrac{d}{dx} \, \sin{x} = \cos{x}$

Differentiation of Cosine function

The derivative of $\cos{x}$ with respect $x$ is equal to negative $\sin{x}$.

$\large \dfrac{d}{dx} \, \cos{x} = -\sin{x}$

Differentiation of Tangent function

The derivative of $\tan{x}$ with respect $x$ is equal to square of $sec{x}$.

$\large \dfrac{d}{dx} \, \tan{x} = \sec^2{x}$

Differentiation of Cotangent function

The derivative of $\cot{x}$ with respect $x$ is equal to negative of square of $\csc{x}$.

$\large \dfrac{d}{dx} \, \cot{x} = -\csc^2{x}$

Differentiation of Secant function

The derivative of $\sec{x}$ with respect $x$ is equal to product of $sec{x}$ and $tan{x}$.

$\large \dfrac{d}{dx} \, \sec{x} = \sec{x} \tan{x}$

Differentiation of Cosecant function

The derivative of $\csc{x}$ with respect $x$ is equal to negative of product of $\csc{x}$ and $\cot{x}$.

$\large \dfrac{d}{dx} \, \csc{x} = -\csc{x} \cot{x}$



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