Limit $ \lim_{x \to 1} \frac{x^{\frac{1}{3}}-1}{\sqrt{x}-1}$ $ \lim_{x \to 1} \frac{x^{\frac{1}{3}}-1}{\sqrt{x}-1}$
How would I solve this limit question? Thanks in advance.

Setting $f(x)=x^{\frac{1}{3}}$ and $g(x)=\sqrt{x}$, we can rewrite the limit as 
$$ \lim_{x\to 1}\frac{x^{\frac{1}{3}}-1}{x-1}\lim_{x\to 1}\frac{x-1}{\sqrt{x}-1}=\frac{f^{\prime}(1)}{g^{\prime}(1)}=\frac{2}{3}$$
