Question

Hello friends!!!....Plzz tell me the answer....
How to differentiate x^x

Answer 1

Hi...☺

Here is your answer...✌

$let \: \: y = {x}^{x} \\ now \: we \: have \: to \: find \: \: \frac{dy}{dx} \:$

Applying log on both sides
We get,

$log(y) = log( {x}^{x} ) \\ \\ log(y) = x log(x) \\ \\ differentiating \: both \: sides \: w.r.t. \: x \\ we \: get \\ \\ \frac{1}{y} \times \frac{dy}{dx} = 1. log(x) + x. \frac{1}{x} \\ \\ \frac{dy}{dx} = y (log(x) + 1) \\ \\ \frac{dy}{dx} = {x}^{x} ( log(x) + 1)$