Solution: Find iJwliJu and iJwlav by (1) and (2). Check the result by substitution and
Chapter 9, Problem 9.6(choose chapter or problem)
Find iJwliJu and iJwlav by (1) and (2). Check the result by substitution and differentiation. (Show the details.)(Partial derivatives on a surface) Let w = f(x, y, z),and let z = g(x, y) represent a surface S in space. Thenon S, the function becomes w(x, y) = f[x, y, g(x, y)].Show that its partial derivatives are obtained fromaw af af iJg -=-+--iJx ax az ax'aw af af ag -=-+--ay ay az a)'[;: = g(x. y)].Apply this to f = x 3 + )'3 + Z2, g = x 2 + y2 andcheck by substitution and direct differentiation. (Thegeneral formula will be needed in Sec. 10.9.)
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