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

Formula

The derivative of tan x, [tan x]',
is sec2 x.
(not cot x)

Example

Example

Solution

x2 tan x is the product of x2 and tan x.

So the derivative of the product is,
the derivative of x2, 2x1
times tan x
plus
x2
times, the derivative of tan x, sec2 x.

Arrange the expression.

So 2x tan x + x2 sec2 x is the derivative of x2 tan x.