Differentiate $e^{x^{3}}$ w.r.t. $x$

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Solution

Let $y = e^{x^{3}}$

Differentiating both sides w.r.t. $x$ , we get,

$\frac{d y}{d x} = \frac{d (e^{x^{3}})}{d x}$

$\frac{d y}{d x} = e^{x^{3}} \times \frac{d (x^{3})}{d x}$

$(using chain rule \frac{d y}{d x} = \frac{d y}{d u} \times \frac{d u}{d x})$

$\frac{d y}{d x} = e^{x^{3}} \times 3 x^{2}$

$\frac{d y}{d x} = 3 x^{2} e^{x^{3}}$

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