alternative proof of derivative of

The typical derivative formula

$$\frac{df}{dx}=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}$$

combined with the binomial theorem yield an alternative way to prove that

$$ \frac{d}{dx}(x^n)=nx^{n-1}$$

for any positive integer $n$ .

Proof.

alternative proof of derivative of is owned by Warren Buck.