Solved: Differentiability In Exercises 43 and 44, use the function to show that and both
Chapter 13, Problem 44(choose chapter or problem)
Differentiability In Exercises 43 and 44, use the function to show that \(f_{x}(0,0)\) and \(f_{y}(0,0)\) both exist, but that f is not differentiable at (0, 0)
\(f(x, y)= \begin{cases}\frac{5 x^{2} y}{x^{3}+y^{3}}, & (x, y) \neq(0,0) \\ 0, & (x, y)=(0,0)\end{cases}\)
Text Transcription:
f_x (0, 0)
f_y (0, 0)
f(x, y) = {5 x^{2} y / x^3 + y^3, (x, y) neq (0, 0) \\ 0, (x, y) = (0, 0)
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