Question

Differentiate the following functions with respect to x:
$x^5{e}^x+x^{6}logx$

Answer 1

We have,

$=\frac{d}{dx}(x^5{e}^x+x^{6}logx)$

$=e^x\frac{d{x}^5}{dx}+x^5\frac{d{e}^5}{dx}+logx\frac{d}{dx}\left(x^6\right)+x^6\frac{d}{dx}\left(logx\right)$ [Using product rule]

$=e^x\times 5x^4+x^5\times e^x+logx\times 6x^5+x^6\times \frac{1}{x}$

$=(5x^4\times e^x+x^5\times e^x+6x^5\times logx+x^5)$

$=x^4(5e^x+e{x}^x+6xlogx+x)$