How do you differentiate f(x) =x(x+3)^3? using the chain rule?

1 Answer
Oct 30, 2015

I found: f'(x)=(x+3)^2(4x+3)

Explanation:

I would use the Chain and Product Rule to deal with the multiplication between the two functions x and (x+3)^3;
I would then use the Chain Rule (in red) to deal with (x+3)^3 deriving first the cube leaving the argument as it is and multiplying the derivative of the argument inside the bracket:

f'(x)=1*(x+3)^3+x*color(red)(3(x+3)^2*1)=
=(x+3)^2[(x+3)+3x]=
=(x+3)^2(4x+3)