Question

Differentiate the following functions with respect to x :

$\frac{1}{sinx}+2^{x+3}+\frac{4}{lo{g}_{x}3}$

Answer 1

We have,

$\frac{d}{dx}(\frac{1}{sinx}+2^{x+3}+\frac{4}{lo{g}_{x}3})$

$=\frac{d}{dx}cosecx+2^3\frac{d}{dx}\left(2^x\right)+\frac{4}{log3}\times \frac{d}{dx}\left(logx\right)[\because lo{g}_{b}a=\frac{loga}{logb}]$

$=-cosecx.cotx+{8.2}^{x}log2+\frac{4}{log3}\times \frac{1}{x}[\because \frac{d}{dx}(a^x)=a^{x}loga]$

$=-cosecxcotx+2^{x+3}log2+\frac{4}{xlog3}$