# Prove the general power rule of derivatives using the inverse

Prove the general power rule of derivatives using the inverse property $\left({x}^{n}={e}^{n\mathrm{ln}x}\right)$?

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Step 1
The general power rule:
$\frac{d}{dx}\left({x}^{n}\right)=n{x}^{n-1}$
Step 2
Proof:

$={e}^{n\mathrm{ln}x}\frac{d}{dx}\left(n\mathrm{ln}x\right)$
$={e}^{n\mathrm{ln}x}\frac{n}{x}$

$=n{x}^{n-1}$
Thus, the general power rule proved.