Hi I need to find the derivative of $\displaystyle \frac{1}{\sqrt{1-x^2}}$.I found it as:

$\displaystyle \frac{d}{dx} (\frac{1}{\sqrt{x^{2}-1}})\newline$

$\displaystyle \frac{d}{dx} (x^{2}-1)^{-\frac{1}{2}}=-\frac{1}{2}(x^{2}-1)^{-\frac{1}{2}-1} \newline$

$\displaystyle =-\frac{1}{2(x^2-1)^\frac{3}{2}}$

But the answer by the book is $\displaystyle -\frac{x}{(x^2-1)^\frac{3}{2}}$

Help.