Question

Differentiate the following with respect to x


e^x/log x

Answer 1

$let \space y= \frac{e^x}{logx}\\differentiating \space both \space sides \space w.r.t \space to \space 'x'...we \space get$

$\frac{dy}{dx}= \frac{logx*\frac {d}{dx}e^x - e^x*\frac{d}{dx}logx}{(logx)^2}\\$ ( using quotient rule of differentiation i.e $\frac {d}{dx}(u/v) = \frac{v*\frac{du}{dx} - u*\frac{dv}{dx} }{v^2}$ )

$or, \frac{dy}{dx}= \frac{logx*e^x - e^x*1/x}{(logx)^2}\\$

$or, \frac{dy}{dx}=\frac{ e^x [logx \space - \space 1/x]}{(logx)^2}$ (ANSWER)