Question

Differentiate the following functions w.r.t. $x$ :
$e^{xloga}+e^{alogx}+e^{aloga}$

Answer 1

Let $y=e^{x\log a}+e^{a\log x}+e^{a\log a}$

$⟹y=e^{\log a^x}+e^{\log x^a}+e^{\log a^a}=a^x+x^a+a^a$

Differentiating on both sides w.r.t $x$

$\frac{dy}{dx}=a^x\log a+a{x}^{a-1}+0=a^x\log a+a{x}^{a-1}$