Question

Differentiate the following functions with respect to x :

$lo{g}_{3}x+3lo{g}_{3}x+2tanx$

Answer 1

We have,

$\frac{d}{dx}f\left(x\right)=\frac{d}{dx}(lo{g}_{3}x+3lo{g}_{3}x+2tanx)$

$=\frac{1}{log3}\frac{d}{dx}\left(logx\right)+3\frac{d}{dx}\left(logx\right)+2\frac{d}{dx}\left(tanx\right)[\because lo{g}_{3}x=\frac{logx}{log3}]$

$=\frac{1}{log3}\times \frac{1}{x}+\frac{3}{x}+2se{c}^{2}x=\frac{1}{xlog3}+\frac{3}{x}+2se{c}^{2}x$