Differentiation of Trigonometric functions

The trigonometric functions are often appeared in differential calculus. So, it is important to learn the differentiation of all trigonometric functions because they are used as formulas in calculus to deal trigonometric functions easily.

Sin function

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

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

Cos function

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

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

Tan function

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

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

Cot function

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

$\dfrac{d}{dx}{\cot{x}} \,=\, -\csc^2{x}$ (or) $-\operatorname{cosec}^2{x}$

Sec function

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

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

Csc (or) Cosec function

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

$\dfrac{d}{dx}{\csc{x}} \,=\, -\csc{x}.\cot{x}$ (or) $-\operatorname{cosec}{x}.\cot{x}$