Answer is done but need help 

We have
\[g(x)=7f(x)+x^2 f(x).\]

First take a derivative from both sides of the above equation to get
\[g'(x)=[7f(x)+x^2 f(x)]'= [7f(x)]'+[x^2 f(x)]'\]
\[=7f'(x)+[x^2]' f(x)+x^2 [f(x)]'      \text{(we have used the product rule)}\]
\[=7f'(x)+2xf(x)+x^2f'(x).\]
Hence
\[g'(x)=7f'(x)+2xf(x)+x^2f'(x).\]
Substitute $x$ by $10$ and use the given assumptions $f(10)=-1$ and $f'(10)=-2$ to get
\[g'(10)=7f'(10)+2(10)f(10)+(10)^2f'(10)\]
\[=7(-2)+20 (-1)+100(-2)=-14-20-200=-234.\]
Hence $g'(10)=-234$.