# Derivative of tan x

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

## Formula

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

is sec^{2} x.

(not cot x)

## Exampley = x^{2} tan x, y' = ?

Solution

Solution (Detail)

x^{2} tan x

is the product of x^{2} and tan x.

So the derivative of the product is,

the derivative of x^{2}, 2x^{1}

times tan x

plus

x^{2}

times, the derivative of tan x, sec^{2} x.

Arrange the expression.

So

2x tan x + x^{2} sec^{2} x

is the derivative of x^{2} tan x.