Answer to Question #249199 in Calculus for moe

Question #249199

True or false:


There is a function  "z"  whose partial derivatives are "\\displaystyle{\\frac{\\partial z}{\\partial y}}=x" and  "\\displaystyle{\\frac{\\partial z}{\\partial x}}=-y"


1
Expert's answer
2021-10-25T18:51:17-0400

Since, the partial derivative of z with respect to y is iota (which is not in real), we can not get any complex number while differentiate a real valued function.

"\\space \\frac{\\partial z}{\\partial y}=i.\\\\\n\\text{Therefore, the given statement is false.}"


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