Question

How do you differentiate # f(x) = sec(x^2 + 1)^2 #?

Answer 1

`f'(x)=4x*sec(x^2+1)^2*tan(x^2+1)`

Explanation:

`d/dx[sec(u)] = sec(u)*tan(u)*u'`

Using the above rule, we can differentiate:
`f(x)=sec(x^2+1)^2`
`f'(x)=2sec(x^2+1)*d/dx[sec(x^2+1)]`
`=2sec(x^2+1)*sec(x^2+1)*tan(x^2+1)*d/dx[x^2+1]`
`=2sec(x^2+1)*sec(x^2+1)*tan(x^2+1)*2x`

Simplifying gives:
`f'(x)=4x*sec(x^2+1)^2*tan(x^2+1)`