Can the square of the derivative $(dy/d\xi)^2$ in the following expression
$$ \frac{dc}{d\xi} = \frac{1}{2}\frac{d}{d\xi}\left(\frac{d y}{d \xi}\right)^2+\frac{2}{\xi +\kappa a}\left(\frac{d y}{d\xi}\right)^2 $$
be factored out like so:
$$ \frac{dc}{d\xi} = \left(\frac{d y}{d \xi}\right)^2\left(\frac{1}{2}\frac{d}{d\xi}+ \frac{2}{\xi +\kappa a}\right)? $$
My intuition is telling me that this is not possible.