If d/dx {f(f(x^2))} = x^6, find f'(x^2)?

Answer 1

So, the derivative of f(f(x²)) = f '(f(x²))•(f '(x²))•2x and since that is x⁶ then:

f '(f(x²))•(f '(x²))•2x = x⁶

f '(f(x²))•(f '(x²)) = x⁵/2

f '(x²) = x⁵/[2•f '(f(x²))]