<s>[INST] derivative of $y=(x^2+x^3)^4$ I can't figure out where I am going wrong.
$$y=(x^2+x^3)^4$$
chain rule it first
$$4(x^2+x^3)^3* \frac d{dx}(x^2+x^3)$$
which should become:
$$4(x^2+x^3)^3(2x+3x^2)$$
factoring out should give me:
$$4*x^2*x(1+x)^3(2+3x)$$
which to me says the answer is: $4x^3(1+x)^3(2+3x)$ 
but the book says: $4x^7(1+x)^3(2+3x)$
where did I go wrong?
 [/INST] Your mistake is in the factoring out. When you factor $x^2$ out from the $(x^2+x^3)^3$ term, it becomes $(x^2)^3(1+x)^3=x^6(1+x)^3$ instead of $x^2(1+x)^3$
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