\[\frac{\mathrm{d}}{\mathrm{d}t}f(x(t),y(t))=\frac{\partial f}{\partial x}\frac{%
\mathrm{d}x}{\mathrm{d}t}+\frac{\partial f}{\partial y}\frac{\mathrm{d}y}{%
\mathrm{d}t},\]