Step 1 :\( \frac{\partial f(x, y)}{\partial x} =4\left(x^{2}-y^{3}\right)^{3}(2x) \)
Step 2 :\( \frac{\partial f(x, y)}{\partial y} =4\left(x^{2}-y^{3}\right)^{3}(-3y^{2}) \)
Step 3 :\( \frac{\partial f(x, y)}{\partial x} =\frac{1}{y} + \frac{y}{x^{2}} \)
Step 4 :\( \frac{\partial f(x, y)}{\partial y} =-\frac{x}{y^{2}} - \frac{1}{x} \)
Step 5 :\( \frac{\partial f(x, y, z)}{\partial x} =ye^{xy}\ln(xz)+\frac{e^{xy}}{x}\ln(xz) \)
Step 6 :\( \frac{\partial f(x, y, z)}{\partial y} =xe^{xy}\ln(xz) \)
Step 7 :\( \frac{\partial f(x, y, z)}{\partial z} =e^{xy}\frac{1}{z} \)