so I have a problem with my teacher's notes and they have confused me. take this equation \begin{align} \lim _{x\to0} \frac{\arcsin x}{ \sin x} \end{align}
if we do the derivative of the top and bottom using l'hopitals rule we get
\begin{align} (\arcsin x)'= \frac{1}{ \sqrt{1-x^2}} \end{align} \begin{align} (\sin x)'= \cos x \end{align}
but when my teacher put them together she did't explain how she somehow got this. \begin{align} \lim _{x\to0} \frac{\sqrt{1-x^2}}{ \cos x} \end{align}
Please help this makes no sense to me, why is the numerator no longer a fraction?
align
when you are writing a single equation. $\endgroup$