Question

Differentiate the following functions with respect to x:
$x^{n}tanx$

Answer 1

We have,

$\frac{d}{dx}\left(x^{n}tanx\right)$

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

$=tanx.n{x}^{n-1}+x^{n}se{c}^{2}x$

$=x^{n-1}(n.tanx+x.se{c}^{2}x)$

$=[x^n=x^{n-1}.x^1=x^{n-1+1}]$