Find $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}$ and $\frac{de{l}^{3}f}{del{y}^2\text{d}\text{e}\text{l}\text{x}}$ for $f(x,y)=x^4{e}^{3xy}.$

Find $\frac{\text{d}\text{e}\text{l}\text{g}}{\text{d}\text{e}\text{l}\text{x}}$ and $\frac{de{l}^{2}g}{\text{d}\text{e}\text{l}\text{y}\text{d}\text{e}\text{l}\text{x}}$ for $g(x,y)=co{s}^5{x}^6{y}^7.$