If-y-x-x-find-dy-dx-

Question Number 10712 by Saham last updated on 23/Feb/17

If y = x^{x}, find \frac{dy}{dx}

Answered by mrW1 last updated on 23/Feb/17

y = x^{x}

\ln y = x \ln x

\frac{1}{y} \times \frac{d y}{d x} = \ln x + 1

\Rightarrow \frac{d y}{d x} = y (\ln x + 1) = x^{x} (1 + \ln x) = x^{x} + x^{x} \ln x

Commented by Saham last updated on 23/Feb/17

God bless you sir .

Answered by mrW1 last updated on 23/Feb/17

a n o t h e r w a y :

y = x^{x} = e^{x \ln x}

\frac{d y}{d x} = e^{x \ln x} \times (\ln x + 1) = x^{x} (1 + \ln x)

Commented by Saham last updated on 23/Feb/17

God bless you sir .

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