If I let f be continuously differentiable on R^2, how do I prove that gradf = (fx,fy)?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.2: Integration By Parts
Problem 41E
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If I let f be continuously differentiable on R^2, how do I prove that gradf = (fx,fy)?

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