If f(x) + x^2[f(x)]^4 = 18 and f(1) = 2, find f '(1).

Question

f ''(1) =

please explain and show answer

Answer 1

We differentiate this equation: f'(x) + 2x[f(x)]⁴ + 4x²[f(x)]³f'(x) = 0.

Now, f'(1) + 2·2⁴ + 4·2³f'(1) = 0; 33f'(1) = - 32; f'(1) = - 32/33