Question

((1/x-y)/(x² y²))dx (x/(x² y²))dy = 0

Answer 1

To solve the given expression ((1/x-y)/(x² y²))dx (x/(x² y²))dy = 0, we can use the concept of partial differentiation.

Step-by-step explanation:

The given expression is ((1/x-y)/(x² y²))dx (x/(x² y²))dy = 0. To solve this expression, we can use the concept of partial differentiation. Let's start by finding the partial derivative with respect to x:

d/dx((1/x-y)/(x² y²))dx = d/dx(dx/(x³ y² - xy³)) = d/(x³ y² - xy³)

Now, let's find the partial derivative with respect to y:

d/dy((1/x-y)/(x² y²))dx = d/dy(dy/(x³ y² - xy³)) = d/(x³ y² - xy³)

Since the given expression is equal to zero, we can set the partial derivatives equal to each other:

d/(x³ y² - xy³) = d/(x³ y² - xy³)

This means that the expression (1/x-y)/(x² y²)dx (x/(x² y²))dy = 0 is satisfied when the partial derivatives with respect to x and y are equal.