Question

Find f'(x) for f(x)=sec^2x^2

Answer 1

I interpret that as

f(x) = ( sec(x^2) )^2

so f'(x) = 2(sec(x^2))*(sec(x^2))(tan(x^2))*(2x)
= 4x(sec(x^2) )^2 ( tan(x^2 )

Answer 2

where did you get the (2x) at the end from?

Answer 3

Chain rule:
df(x^2)/dx
=df(x^2)/d(x^2).dx^2/dx
=df(x^2)/d(x^2).2x