Question

If y=x^x, Find dy/dx
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Answer 1

$y = {x}^{x} \\ \frac{dy}{dx} = x. {x}^{x - 1}$

HOPE THIS HELPS....

Answer 2

f(x) = x^x

f(x + h) = (x^(x + h))

lim [f(x + h) - f(x) ]/h

h->0

lim [ x^(x + h) - x^x ] /h

h->0

lim x^x ( x^h - 1) / h

h ->0

x^x × lim (x^h - 1)/h

h->0

By logrithmic limit limx->0 (a^x - 1)/x = loga

•°• = x^x × logx

f'(x) = x^x × logx

dy/dx = x^x × logx is Answer