If f(x)+x^2(f(x))^3=10 and f(1)=2, then find derivative of f(1)

Answer 1

f(x) + x²[f(x)]³ = 10

Using the Product Rule and Chain Rule, we have: f'(x) + 2x[f(x)]³ + x²(3[f(x)]²f'(x)) = 0

So, when x = 1, we get f'(1) + 16 + 12f'(1) = 0

13f'(1) = -16

f'(1) = -16/13