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2. IShow, using the definition of the derivative, that the function f(x, y) differentiable at every point (xo, Yo) E R². xy is Note: If you argue that f is differentiable because of continuity of its partial derivatives, you will receive zero points

2. IShow, using the definition of the derivative, that the function f(x, y) differentiable at every point (xo, Yo) E R². xy is Note: If you argue that f is differentiable because of continuity of its partial derivatives, you will receive zero points

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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2. IShow, using the definition of the derivative, that the function f(x, y) = xy² is differentiable at every point (xo, Yo) E R². Note: If you argue that f is differentiable because of continuity of its partial derivatives, you will receive zero points. Hint: Clearly the partial derivatives of f exist and are continuous, so we know from lec- tures that the derivative will exist and it will be given by A(xo, Yo) = (ô=f(xo,yo), Ôy ƒ (xo,Yo)).
Transcribed Image Text:2. IShow, using the definition of the derivative, that the function f(x, y) = xy² is differentiable at every point (xo, Yo) E R². Note: If you argue that f is differentiable because of continuity of its partial derivatives, you will receive zero points. Hint: Clearly the partial derivatives of f exist and are continuous, so we know from lec- tures that the derivative will exist and it will be given by A(xo, Yo) = (ô=f(xo,yo), Ôy ƒ (xo,Yo)).
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