Question

Differentiate the following functions with respect to x :

$e^{x}loga+e^{a}logx+e^{a}loga$

Answer 1

We have,

$\frac{d}{dx}(e^{x}loga+e^{a}logx+e^{a}loga)$

$=\frac{d}{dx}\left(e^{xloga}\right)+\frac{d}{dx}\left(e^{alogx}\right)+\frac{d}{dx}\left(e^{aloga}\right)$

$=e^{xloga}.loga+e^{alogx}.\frac{a}{x}+0$

$[\because a.e^{xloga}\text{is constant}]$

$=loga.e^{xloga}+\frac{a}{x}{e}^{alogx}$

$=loga.a^x+\frac{a}{x}{x}^a$

$\left[a^x\text{can be written as}{e}^{xloga}\right]$

$=a^{x}loga+a{x}^{a-1}$