Differentiate $f(x,y)=x^2{e}^{-2y}$ with respect $tox.$

Differentiate $f(x,y)=a{x}^2{e}^{-by}$ with respect $toy.$

Compute the second derivative $off(t)=e^{-at}cos(bt)$ with respect $tot.$

Calculate the derivative $of[sin((t)){]}^2$ with respect $tot.$

Calculate the derivative $ofk\frac{[x(t){]}^2}{2}+m\frac{[x^{}(t){]}^2}{2}$ with respect $tot,$ with $k$ and $m$ constants.