L'Hopital's Rule

When calculating the limits of some $\frac{0}{0}$ form, for example,

$$\lim_{x\to a} \frac{f(x)}{g(x)}$$

with $f(a)=g(a)=0$, we can use this rule. The answer should be $\frac{f'(x)}{g'(x)}$. We can use $\frac{df(x)}{dg(x)}$ at the point a to represent the value,

$$ \frac{df(x)}{dg(x)} = \frac{\frac{df(x)}{dx}}{\frac{dg(x)}{dx}} = \frac{f'(x)}{g'(x)} $$.