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

1 Answer
Jul 2, 2017

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)