Question

d/dx (logx ^e)=?
What is the answer for the question?​

Answer 1

Answer:

$let \: y \: = log( {x}^{e} ) \\ = > y = e log(x) \\ now ,\: differentiating \: both \: sides \: w.r.to \: x, \: we \: get \: \\ = > \frac{dy}{dx} = e \times \frac{1}{x} \\ = \frac{e}{x}$

$so, \: \frac{d}{dx} log( {x}^{e} ) = \frac{e}{x}$

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Formula used :

$● log( {x}^{y} ) = y log(x) \\ ● \frac{d}{dx} log(x) = \frac{1}{x}$