Is there a function f : R^2 \to R whose partial derivatives are \frac {\delta f}{\delta x} = x +...

Question:

Is there a function {eq}f : R^2 \to R {/eq} whose partial derivatives are {eq}\frac {\delta f}{\delta x} {/eq}= x + 4y and {eq}\frac {\delta f}{\delta y} {/eq}= 3x - y? If so, find this function and if not, explain why it can't exist.

Mixed Partial Derivatives:

For a real valued twice continuously differentiable function, we have:

{eq}\displaystyle \frac{\partial ^2f}{\partial x\partial y}=\frac{\partial ^2f}{\partial y\partial x}\\ {/eq}

We will use this fact to solve this problem.

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

If such a function f exists, then we would have:

{eq}\displaystyle \frac{\partial ^2f}{\partial x\partial y}=\frac{\partial ^2f}{\partial y\partial...

See full answer below.


Learn more about this topic:

Loading...
The Chain Rule for Partial Derivatives

from

Chapter 14 / Lesson 4
36K

This lesson defines the chain rule. It goes on to explore the chain rule with partial derivatives and integrals of partial derivatives.


Related to this Question

Explore our homework questions and answers library