Problems

In Problems 1-8, find ∂z/∂x and ∂z/∂x by the Chain Rule.

In Problems 9-14, find dy/dx.

In Problems 15-22, find the tangent line and the slope of the curve at the given point.

In Problems 23-26 find and

In Problems 27-32, find the tangent plane to the surface at the given point.

In Problems 33-38, find ∂z/∂x and ∂z/∂y.

39            Suppose that x items can be bought at a price of y dollars per item, where y depends on x in such a way that dy/dx = -1/(1 + √x). Find the rate of change of the total cost z = xy with respect to x.

40            A point moves along the parabola y = x². Find the rate of change with respect to x of the distance from the origin.

41             Suppose w depends on x, y, and z, and both y and z depend on x. Find a formula for dw/dx using the Chain Rule.

42            Suppose z depends on x and y, while y depends on x and f. Use the Chain Rule to find a formula for