Question

Differentiate the following w.r.t $x{e}^x\left[log\right(a\left)\right]+e^a\left[log\right(x\left)\right]+e^a\left[log\right(a\left)\right]$

Answer 1

$y=e^{x}log\left(a\right)+e^{x}logx+e^{a}loga\frac{d}{dx}=\frac{d}{dx}\left(e^{x}log\right(a)+e^{a}logx+e^{a}loga)=\frac{d}{dx}\left(e^{x}log\right(a\left)\right)+\frac{d}{dx}\left(e^{a}logx\right)+\frac{d}{dx}\left(e^{a}loga\right)\Rightarrow e^x\frac{d}{dx}\left(loga\right)+\frac{d}{dx}\left(e^x\right)loga+e^a\frac{d}{dx}\left(logx\right)+0\to e^x.0+e^{x}loga+e^a\frac{1}{x}+0\frac{dy}{dx}=1e^{x}loga+\frac{e^a}{x}$