Question

If 76+2f(x)+x^2(f(x))^3=0 and f(3)=-2, find f'(3).

f'(3)=

Answer 1

2f'(x)+2x(f(x))^3+3x^2(f'(x))=0
f(3)=-2, x=3
2f'(3)+2*3*-2^3+3*-2^2*f'(3)=0
2f'(3)-48+12f'(3)=0
14f'(3)=48
f'(3)=48/14=24/7