Amina Wilkinson

2022-12-05

General formula for $n$-th derivative of ${e}^{f\left(x\right)}?$
Let $g\left(x\right)={e}^{f\left(x\right)}$ where $f$ is infinitely differentiable function. Does there exist a formula for $n$-th derivative ${g}^{\left(n\right)}\left(x\right)$ where $n\ge 0?$

Aleah Rowe

Expert

Hint:
$\mathrm{ln}\left(y\right)=f\left(x\right)$
in order to obtain a higher derivative.

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