find f prime of 1

Question

If f (x) − x³ [ f (x)]³ = −5x − 1 and f (1) = 2, find f '(1).

Answer 1

f'(x) - 3x²[f(x)]³ - 3x³[f(x)]²f'(x) = - 5; at x = 1 we have: f'(1) - 3·1²·2³ - 3·2²·1³ ·f'(1) = - 5; - 11f'(1) = 19;

f'(1) = - 19/11