Use the definition of a partial derivative to find f_x(0, 0) and f_y(0, 0). f(x, y) = { 2x^2y^2 / (x^2 + 7y^2) if (x, y) ? (0, 0) 0 if (x, y) = (0, 0) } f_x(0, 0) = f_y(0, 0) =
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Step 1: Using the definition of partial derivative, we have: \[f_x(x, y) = 2x^2y^2 \text{ if } (x, y) \neq (0, 0)\] \[f_x(x, y) = x^2 + y^2 \text{ if } (x, y) = (0, 0)\] Show more…
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