Question: Explain why the function is differentiable at the given point. f ( x, ) = 3 + x In(xy - 5), (3, 2) The partial

Explain why the function is differentiable at the given point. f ( x, ) = 3 + x In(xy - 5), (3, 2) The partial derivatives are f (x, y) = In(xy -5 ) + - yx xy and f (x, y) = , so fx(3, 2) = 6 and f (3, 2) = 9 . Both f and f are continuous functions for xy > 5 V , so f is differentiable at (3, 2). Find the linearization L(x, y) of f(x, y) at (3, 2). L ( X , y ) = 6x + 9y - 35 X

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