Question

derivative of e raise to power 2 log x​

Answer 1

y=$e^{2(log(x))}$

Taking log o.b.s

log(y)=log($e^{2(log(x))}$)

          =2logx*(e^2)

diff. w.r.t.x

$\frac{1}{y}$*$\frac{dy}{dx}$=[2logx*$\frac{d}{dx}$e^2]+[e^2 * $\frac{d}{dx}$2logx]

      =y*{[2logx*e^2]+[e^2*(2/x)]

       =$e^{2(log(x))}${[2 log(x) * $e^{2}$] + [ $e^{2}$ * $\frac{2}{x}$]}

$\frac{d(e^{2 log (x)} }{dx}$ = $e^{2(log(x))}${[2 log(x) * $e^{2}$] + [ $e^{2}$ * $\frac{2}{x}$]}