What is the derivative of $x^{7 x}$ $x^(7x)$ ?

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What is the derivative of $x^{7 x}$ $x^(7x)$ ?

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Answer 1 · 2016-07-17T23:04:35

Rewrite this as $e^{7 x \cdot ln x}$ $e^(7x*lnx)$ Hence the derivative is

$d \frac{e^{7 x \cdot ln x}}{d x} = e^{7 x \cdot ln x} \cdot [7 \cdot ln x + 7 x \cdot \frac{1}{x}] = 7 \cdot e^{7 x \cdot ln x} \cdot [ln x + 1] = 7 \cdot x^{7 x} \cdot (ln x + 1)$ $d(e^(7x*lnx))/dx=e^(7x*lnx)*[7*lnx+7x*1/x]=7*e^(7x*lnx)*[lnx+1]= 7*x^(7x)*(lnx+1)$

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What is the derivative of $x^{7 x}$ $x^(7x)$ ?

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