Originally Posted by
Reckoner Are you differentiating with respect to $\displaystyle t$ or with respect to $\displaystyle x$?
For $\displaystyle \frac{d}{dt}\left[\omega\sqrt{A^2 - x^2}\right]$ we have
$\displaystyle \frac{d}{dt}\left[\omega\sqrt{A^2 - x^2}\right] = \frac{d}{dt}\left[\omega\left(A^2 - x^2\right)^{1/2}\right]$
$\displaystyle = \frac{\omega}2\left(A^2 - x^2\right)^{-1/2}\frac{d}{dt}\left[A^2 - x^2\right]$
$\displaystyle = \frac{\omega}2\left(A^2 - x^2\right)^{-1/2}\left(-2x\frac{dx}{dt}\right)$
Then you can simplify a bit.