Question

For the equation given, find dy/dx: 7x3y2 − 7x2y = 3

Answer 1

To find dy/dx for the given equation 7x^3y^2 - 7x^2y = 3, apply implicit differentiation by differentiating both sides of the equation with respect to x and solving for dy/dx.

Step-by-step explanation:

To find dy/dx for the given equation 7x^3y^2 - 7x^2y = 3, we need to use implicit differentiation. Implicit differentiation is used when we have an equation in which y is not explicitly written as a function of x. Here are the steps:

1. Differentiate both sides of the equation with respect to x.
2. Apply the chain rule when differentiating y terms.
3. Combine similar terms and solve for dy/dx.

After following these steps, you will find the derivative dy/dx for the given equation.

Answer 2

The value of dy/dx is
`(3x - 7xy^2)/(7x^2y - 14x^3y).`

Step-by-step explanation:

To find the derivative of the equation
`7x^3y^2 - 7x^2y = 3`, we can use implicit differentiation. Implicit differentiation is a method of differentiation that is used when one or more variables in an equation are not explicitly defined in terms of another variable.

In this case, y is not explicitly defined in terms of x. Therefore, we need to use implicit differentiation to find dy/dx.

To do this, we first take the derivative of both sides of the equation with respect to x. This gives us:

`21x^2y^2 + 7x^3(2y)dy/dx - 14x^2y + 7x^2(dy/dx) = 0`

Next, we can move all of the terms that contain dy/dx to one side of the equation, and all of the other terms to the other side of the equation. This gives us:

`7x^2(dy/dx) = -21x^2y^2 - 7x^3(2y) + 14x^2y`

Finally, we can solve for dy/dx by dividing both sides of the equation by
`7x^2.` This gives us:

`dy/dx = (3x - 7xy^2)/(7x^2y - 14x^3y)`

Therefore, the derivative of the equation
`7x^3y^2 - 7x^2y = 3` is
`dy/dx = (3x - 7xy^2)/(7x^2y - 14x^3y).`