Question

Differentiate the following functions with respect to x:
$x^2{e}^{x}logx$

Answer 1

We have,

$\frac{d}{dx}\left(x^2{e}^{x}logx\right)$

$=e^{x}logx\frac{d}{dx}\left(x^2\right)+x^{2}logx\frac{d}{dx}\left(e{x}^2\right)+e^x\frac{d}{dx}\left(logx\right)$ [Using product rule]

$=e^{x}logx.2x+x^{2}logx.e^x+x^2{e}^x.\frac{1}{x}$

$=x{e}^x(2.logx+xlogx+1)$