Let
(a) Use the definition of the partial derivative to find fx (0, 0) and fy(0, 0).
(b) Let a be a nonzero constant and let x(t) = (t, at). Show that f o x is differentiable, and find D( f o x)(0) directly.
(c) Calculate Df (0, 0)Dx(0). How can you reconcile your answer with your answer in part (b) and the chain rule?
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