How can I expand $\frac{1}{\sqrt{1-x^2}}$ by using the binomial series? How can I expand $\frac{1}{\sqrt{1-x^2}}$ by using the binomial series? I know how to expand $\frac{1}{\sqrt{1-x}}$, but I have no idea how to expand $\frac{1}{\sqrt{1-x^2}}$. Simply differentiate this makes expanding way to complicated.

HINT:
$$\frac1{\sqrt{1-x^2}}=(1-x^2)^{-\frac12}$$
