Chapter 12: Q. 21 (page 944)

Let f(x, y) and g(x, y) be functions of two variables with the property that $\frac{\partial f}{\partial x} = \frac{\partial g}{\partial x}$ and $\frac{\partial f}{\partial y} = \frac{\partial g}{\partial y}$ for every point $(x, y) \in R^{2}$ . What is the relationship between f and g?

Short Answer

Expert verified

The relationship is: $f (x, y) = g (x, y)$ .

Step by step solution

Given

Given that: $\frac{\partial f}{\partial x} = \frac{\partial g}{\partial x} and \frac{\partial f}{\partial y} = \frac{\partial g}{\partial y}$

To find

We have to find the relationship between f and g.

Calculation

If $\frac{\partial f}{\partial x} = \frac{\partial g}{\partial x} and \frac{\partial f}{\partial y} = \frac{\partial g}{\partial y}$ then we can say that both x and y parrs of the functions are equal.

We can write it as: $f (x, y) = g (x, y)$

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Let f(x, y) and g(x, y) be functions of two variables with the property that $\frac{\partial f}{\partial x} = \frac{\partial g}{\partial x}$ and $\frac{\partial f}{\partial y} = \frac{\partial g}{\partial y}$ for every point $(x, y) \in R^{2}$ . What is the relationship between f and g?

Short Answer

Step by step solution

Given

To find

Calculation

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Let f(x, y) and g(x, y) be functions of two variables with the property that ∂f∂x=∂g∂xand ∂f∂y=∂g∂yfor every point x,y∈R2. What is the relationship between f and g?

Short Answer

Step by step solution

Given

To find

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Let f(x, y) and g(x, y) be functions of two variables with the property that $\frac{\partial f}{\partial x} = \frac{\partial g}{\partial x}$ and $\frac{\partial f}{\partial y} = \frac{\partial g}{\partial y}$ for every point $(x, y) \in R^{2}$ . What is the relationship between f and g?