<img src="https://tex.z-dn.net/?f=y%20%3D%20%20%7Bx%7D%5E%7Bx%7D%20" id="TexFormula1" title="y = {x}^{x} " alt="y = {x}^{x} "

vodomira [7]

3 years ago

align="absmiddle" class="latex-formula">
Find
$\frac{dy}{dx}$

Mathematics

1 answer:

Yuki888 [10]3 years ago

7 0

Answer:

$y = x^x\\\\log y = x log x\\\\\frac{1}{y} \frac{dy}{dx} = x \cdot \frac{1}{x} + log x\\\\\frac{1}{y} \frac{dy}{dx} = 1 + log x\\\\\frac{dy}{dx} = y (1 + log x)\\\\\frac{dy}{dx} = x^x(1 + log x)$

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