What is the second derivative of f(x) = sec x

We have to find the second derivative of f(x) = sec
x

f'(x) = sec x* tan x

use the
product rule

f''(x) = (sec x * tan
x)'

=> (sec x)'*tan x + sec x*(tan
x)'

=> sec x * tan x*tan x + sec x * (sec
x)^2

=> sec x * (tan x)^2 + (sec
x)^3

=> sec x[(tan x)^2 + (sec
x)^2]

=> sec x[ (tan x)^2 + 1 + (tan
x)^2]

=> sec x*(1 + 2*(tan
x)^2)

The second derivative of f(x) = sec x
is sec x*(1 + 2*(tan x)^2)