91Ó°ÊÓ

For the following exercises, calculate the partial derivatives. \(\frac{\partial z}{\partial x}\) and \(\frac{\partial z}{\partial y}\) for \(z=x^{8} e^{3 y}\)

For the following exercises, calculate the partial derivatives. \(\frac{\partial z}{\partial x}\) and \(\frac{\partial z}{\partial y}\) for \(z=\ln \left(x^{6}+y^{4}\right)\)

For the following exercises, calculate the partial derivatives. Find \(f_{y}(x, y)\) for \(f(x, y)=e^{x y} \cos (x) \sin (y)\)

For the following exercises, calculate the partial derivatives. Let \(z=e^{x y} .\) Find \(\frac{\partial z}{\partial x}\) and \(\frac{\partial z}{\partial y}\)

For the following exercises, calculate the partial derivatives. Let \(z=\ln \left(\frac{x}{y}\right) .\) Find \(\frac{\partial z}{\partial x}\) and \(\frac{\partial z}{\partial y}\)

For the following exercises, calculate the partial derivatives. Let \(z=\tan (2 x-y) .\) Find \(\frac{\partial z}{\partial x}\) and \(\frac{\partial z}{\partial y}\)

For the following exercises, calculate the partial derivatives. Let \(z=\sinh (2 x+3 y) .\) Find \(\frac{\partial z}{\partial x}\) and \(\frac{\partial z}{\partial y}\)

For the following exercises, calculate the partial derivatives. Let \(f(x, y)=\arctan \left(\frac{y}{x}\right)\) . Evaluate \(f_{x}(2,-2)\) and \(f_{y}(2,-2)\)

For the following exercises, calculate the partial derivatives. Let \(f(x, y)=\frac{x y}{x-y} . \quad\) Find \(\quad f_{x}(2,-2) \) and \(f_{y}(2,-2)\)

Evaluate the partial derivatives at point P(0, 1). Find \(\frac{\partial z}{\partial x}\) at \((0,1)\) for \(z=e^{-x} \cos (y)\)