Answer
$e^{x}(x^{3}+3x^{2}-x-1)$
Work Step by Step
a) The power rule states that for any 2 functions u and v, $$\frac{d}{dx}uv=u'v+uv'$$
taking $u=x^{3}-x$ and $v=e^{x}$, $$\frac{d}{dx}(x^{3}-x)e^{x} = (\frac{d}{dx}x^{3}-x)(e^{x})+(\frac{d}{dx}e^{x})(x^{3}-x)$$ $$= (3x^{2}-1)e^{x}+e^{x}(x^3-x)$$ $$=3x^2e^x-e^x+x^3e^x-xe^x$$ $$=x^3e^x+3x^2e^x-xe^x-e^x$$ $$=e^{x}(x^{3}+3x^{2}-x-1)$$
b) See graph (f in blue and f' in red).