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

Using the product rule is not enough. 
$$(x(x^2 + 3x)^3)^\prime = (x)^\prime \cdot (x^2 + 3x)^3 + x \cdot ((x^2 + 3x)^3)^\prime$$
$$=  (x^2 + 3x)^3 + x \cdot ((x^2 + 3x)^3)^\prime$$
For the rigth part you need to use the chain rule. 
$$=  (x^2 + 3x)^3 + x \cdot 3(x^2 + 3x)^2\cdot(x^2+3x)^\prime$$
$$=  (x^2 + 3x)^3 + x \cdot 3(x^2 + 3x)^2\cdot(2x+3)$$
Now you can simplifying the result:
$$=  (x^2 + 3x)^2 \cdot \left((x^2 + 3x) + x \cdot 3\cdot(2x+3)\right)$$
$$=  (x^2 + 3x)^2 \cdot \left(x^2 + 3x + 6x^2 + 9x\right)$$
$$=  (x^2 + 3x)^2 \cdot \left(7x^2 + 12x\right)$$
