If $y=x^{4}cosx.$ what is $d\frac{y}{d}x.$

$(2$ points$)$

$(2$a$)$ If $V=ln(x^2+y^2),$ prove that the partial derivative $de{l}^2\frac{V}{d}el{x}^2+de{l}^2\frac{V}{h}at(c)y^2=0$

$(5$ poinis$)$

$(2$b$)$ Find the partial derivatives $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{z}}$ and $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{y}}$ for the function $Z=(2x-y)(x+3y).$