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.
The derivative of sec x, [sec x]',
is sec x tan x.
y = sec3 x means y = (sec x)3.
This is a composite function of
y = (whole)3 and (whole) = sec 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.