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Chain rule with constraints 1. Let P = (1, 2, 3) and assume f (x, y, z) is a diﬀerentiable function with �f = i − 2j + 3k at P . Also assume that x, y and z satisfy the relation x3 − y 2 + z = 0. Take x and y to be the independent variables and let g(x, y) = f (x, y, z(x, y)). Find �g at the point (1,2). MIT OpenCourseWare http://ocw.mit.edu 18.02SC Multivariable Calculus Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.