Question

What is the second derivative of `f(x)= secx^2`?

Answer 1

`f''(x) = 8x^3 sec^3x^2tanx^2`

Explanation:

Original Function:
`f(x) = secx^2`

Important equations:
`(d sec(x))/(dx) = sec(x)tan(x)`
`(d tan(x))/(dx) = sec^2(x)`

Remember to use chain rule for the `x^2` inside the argument of the trig function!

First derivative:
`f'(x) = 2xsecx^2 tanx^2`

Second derivative:
`f''(x) = 2x(2x)secx^2tanx^2 (2x)sec^2 x^2`
`f''(x) = 8x^3secx^2tanx^2sec^2x^2`
`f''(x) = 8x^3 sec^3x^2tanx^2`