Let f (x, y) = x 2 y x 2 + y2 if (x, y) = (0, 0) 0 if (x, y) = (0, 0) . (a) Use the
Chapter 2, Problem 38(choose chapter or problem)
Let f (x, y) = x 2 y x 2 + y2 if (x, y) = (0, 0) 0 if (x, y) = (0, 0) . (a) Use the definition of the partial derivative to find fx (0, 0) and f y (0, 0). (b) Let a be a nonzero constant and let x(t) = (t, at). Show that f x is differentiable, and find D( f x)(0) directly. (c) Calculate D f (0, 0)Dx(0). How can you reconcile your answer with your answer in part (b) and the chain rule?
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