# Derivative of cot x

How to find the derivative of the given function by using the derivative of cot x: formula, 1 example, and its solution.

## Formula

The derivative of cot x, [cot x]',

is -csc^{2} x.

## Exampley = 7x cot x, y' = ?

Solution

Solution (Detail)

7x cot x

is the product of 7x and cot x.

So the derivative of the product is,

the derivative of 7x, 7

times cot x

plus

7x

times, the derivative of cot x, -csc^{2} x.

+7x⋅(-csc^{2} x) = -7x csc^{2} x

So

7 cot x - 7x csc^{2} x

is the derivative of 7x cot x.