$\displaystyle \int \frac{1}{\sqrt{81-x^2}}~dx$

I know I need to use substitution and I am aware of the fact that $\displaystyle \frac{1}{\sqrt{1-x^2}}$ = derivative of arcsin(x), but I am unsure how I apply these to the above problem.

I have the answer $\displaystyle arcsin \left(\frac{x}{9}\right)+C$ but I don't follow the steps to get to it.