# How do you differentiate f(x)=(x^3-2x)(e^x-x^2) using the product rule?

Jul 3, 2016

$y = \left({x}^{3} - 2 x\right) \left({e}^{x} - {x}^{2}\right)$

$\ln \left(y\right) = \ln \left({x}^{3} - 2 x\right) + \ln \left({e}^{x} - {x}^{2}\right)$

$\frac{y '}{y} = \frac{3 {x}^{2} - 2}{{x}^{3} - 2 x} + \frac{{e}^{x} - 2 x}{{e}^{x} - {x}^{2}}$

$y ' = y \left(\frac{3 {x}^{2} - 2}{{x}^{3} - 2 x} + \frac{{e}^{x} - 2 x}{{e}^{x} - {x}^{2}}\right)$

with $y = \left({x}^{3} - 2 x\right) \left({e}^{x} - {x}^{2}\right)$

it give you

$y ' = \left(3 {x}^{2} - 2\right) \left({e}^{x} - {x}^{2}\right) + \left({e}^{x} - 2 x\right) \left({x}^{3} - 2 x\right)$