Chain Rule Q: x[f(x)]^3 + x^2f(x) = 3, f(2) = 1; find f'(2)

[grapz]

Suppose f is a function such that x[f(x)]^3 + x^2f(x) = 3 and f(2) = 1

find f' (2)

i am not sure how to do this. do i just find the derivative of the first and plug it in?
there is no answer so i'm really stuck.

 

[galactus]

Use the chain rule and product rule. You can sub in your values and solve for f'(2).

\(\displaystyle \L\\x[f(x)]^{3}+x^{2}f(x)=3, \;\ f(2)=1\)

\(\displaystyle \L\\x\underbrace{(3[f(x)]^{2}f'(x))}_{\text{chain rule}}+[f(x)]^{3}+x^{2}f'(x)+f(x)2x\)