Differentiate with product rule Question: differentiate $x(x^2 +3x)^3$
I have gotten to the point where i've used the product rule and i've gotten
$$(x^2 + 3x)^3 + x\cdot(3x+9)(x^2 + 3x)^2$$
but now that it comes to the simplifying im completely at a loss, any help would greatly appreciated

Use the $\color{red}{\text{product rule}}$ and the $\color{blue}{\text{chain rule}}$
$$\begin{array}{rcl}(x(x^2+3x)^3)' &\color{red}{=}& x'\cdot (x^2+3x)^3+((x^2+3x)^3)'\cdot x \\ &\color{blue}{=}& (x^2+3x)^3+x(3(x^2+3x)^2\cdot (x^2+3x)') \\ &=& (x^2+3x)^3+x(3(x^2+3x)^2(2x+3))\\ &=& (x^2+3x)^3+3x(x^2+3x)^2(2x+3)\\ &=&x^3 (x+3)^2 (7 x+12) \end{array}$$ 
