2 3 pts for each of the functions below find the first and second part

Question

2. (3 pts) For each of the functions below, find the first and second partial derivative with respect to eachvariable, as well as the cross-partial derivative (5 derivatives total). The first case is done for you. \text { a. } f(x, y)=5 x^{2} y \text { b. } f\left(x_{1}, x_{2}\right)=x_{1}^{2}-x_{1} x_{2} \text { c. } f\left(x_{1}, x_{2}\right)=3 x_{1}^{\frac{1}{3}} x_{2}^{3} \text { d. } f\left(x_{1}, x_{2}\right)=x_{1}+\frac{x_{2}}{x_{1}} \text { e. } f(x, z)=\frac{5 x+10 z}{x^{3}} \text { f. } f(x, y)=\frac{x y+x^{2}}{x+y} \text { g. } f(x, y)=\sqrt{x^{2}+y}