Derivative of sec x

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

Formula

Formula

The derivative of sec x, [sec x]',
is sec x tan x.

Example

Example

Solution

So the derivative of the composite function is,
the derivative of the outer function (sec x)3, 3(sec x)2
times,
the derivative of the inner function sec x, sec x tan x.

(sec x)2⋅(sec x) = (sec x)3 = sec3 x

So the right side is 3 sec3 x tan x.

So 3 sec3 x tan x is the derivative of sec3 x.