Differentiate the following functions with respect to x:

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

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Solution

We have,

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

$= e^{x} \frac{d}{d x} (x^{3}) + x^{3} \frac{d}{d x} (e^{x})$ [Using product rule]

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

$= x^{2} e^{x} (3 + x)$

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