a Find dhuv using the chain rule b Find dhuv by calculating

a. Find dh(u,v) using the chain rule.

b. Find dh(u,v) by calculating h(u,v). Find a formula for h(u,v) that involves only the variables u,v. Then differentiate that function.

Calculate z x and z y when z = x 2 + 3xy + y 1. Solution. To find z x treat y as a constant and differentiate with respect to x. We have z = x 2 + 3xy + y 1 so z x = 2x + 3y Similarly z y = 3x + 1