$n^{t h}$ derivative of $e^{a x}$ is ________.

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Solution

Take $y = e^{a x}$
$\frac{d y}{d x}$ $= \frac{d (e^{a x})}{d x} = a e^{a x}$
$\frac{d^{2} y}{d x^{2}}$ $= \frac{d (a e^{a x})}{d x} = a^{2} e^{a x}$
Similarly, the $n^{t h}$ derivative will be
$\frac{d^{n} y}{d x} = a^{n} e^{a x}$

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