Find the indicated partial derivative fx for fxy x2y -

Question

Find the indicated partial derivative.

f_x for f(x,y) = x²y - ln(2x-y)

h_xy for h(x,y,z) = xz - x²y³z² - ln(yz)

Find an equation z-z' = f_x(x', y')(x-x') + f_y(x', y')(y-y') of the tangent plane to the surface f(x,y) = tan^-1(y/x) at the point (1, √(3), π/3)

Calculate the total differential dz = f_x dx + f_y dy for f(x,y) = 1 - x sin (y)

Use the Chain Rule to calculate dz/dt if z = xy + e^y, x(t) = te^t, and y(t)=1 - t³.

Find the gradient f for f(x,y) = xy - y² +e^x at the point (0, 3, -8)