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Sum of Coefficients of All Terms

Differentiate...

Question

Differentiate $x^{x}$ with respect to $x log x$ .

x^{x}

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\frac{1}{x}

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x^{x + 1}

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None of these

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Solution

The correct option is A $x^{x}$
$u = x^{x} ⟹ log u = x log x = v$
$⟹ u = e^{v}$
Therefore,
$\frac{d u}{d v} = \frac{d}{d v} (e^{v}) = e^{v} = u$

$⟹ \frac{d u}{d v} = x^{x}$

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