Y = x^x Taking log In y = ln x^x In y = x ln x 1/ydy/dx =ln x +1 dy/dx =y (1+ln x) =x^x (1+ln x) ...

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Implicit Differentiation

Find d y/d x ...

Question

Find $\frac{d y}{d x}$ :
$y = x^{x}$

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Solution

$y = x^{x}$
Taking log
In y = ln $x^{x}$
In y = x ln x
$\frac{1}{y} \frac{d y}{d x} = l n x + 1 \frac{d y}{d x} = y (1 + l n x) = x^{x} (1 + l n x)$

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