is there a way to simplify $x^{2} ( v' (x^{n})' )$? so I have what is probably an algebra question, if I have $x^{2} ( v' (x^{n})' )$ where the ' denotes a derivative, is there a way to simplify this expression? 

Note that $$ \begin {align*} x^2 \cdot v'(x) \cdot \left( x^n \right)' &= x^2 \cdot v'(x) \cdot nx^{n-1} \\&= nx^{n+1} \cdot v'(x), \end {align*} $$ which is as far as you can get if you don't know $v(x)$. 
