The differential of $e^{x^{3}}$ with respect to $l o g_{e} x$ is:

e^{x^{3}}

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3 x^{2} e^{x^{3}}

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3 x^{3} e^{x^{3}}

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3 x^{2} e^{x^{3}} + 3 x^{2}

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Solution

The correct option is C $3 x^{3} e^{x^{3}}$
Differentiating given function w.r.t. $log_{e}x$
$= \frac{d e^{x^{3}}}{d (l o g x)}$
$= \frac{e^{x^{3}} \times 3 x^{2}}{1 / x}$
$= 3 x^{3} e^{x^{3}}$

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