Question

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

Answer 1

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)`