Finding Partial Derivatives Implicitly.

Find dz/dx and dz/dy for

3x^(2)z-x^(2)y^(2)+2z^(3)+3yz-5=0

How would you type this in wolfram alpha calcultor to get the answer?

Thanks,

To find partial derivatives implicitly, you can enter the equation into Wolfram Alpha. Here's how you can type it:

1. Open Wolfram Alpha calculator.
2. In the input box, type "d/dx[3x^2z - x^2y^2 + 2z^3 + 3yz - 5] = 0"
This notation tells Wolfram Alpha that you want to find the partial derivative of the equation with respect to x.
3. Press Enter or click the "Submit" button.

To find dz/dy, do the following:

1. In a new input box, type "d/dy[3x^2z - x^2y^2 + 2z^3 + 3yz - 5] = 0"
This tells Wolfram Alpha to find the partial derivative of the equation with respect to y.
2. Press Enter or click the "Submit" button.

Wolfram Alpha will then provide you with the step-by-step calculations and the final answers for dz/dx and dz/dy.

To find the partial derivatives dz/dx and dz/dy, you can use the chain rule. Here is the step-by-step process:

1. Start by differentiating both sides of the equation with respect to x:
d/dx (3x^2z - x^2y^2 + 2z^3 + 3yz - 5) = 0.

2. Apply the chain rule to each term. For example, for the first term 3x^2z, we have:
- Over the variable z, the derivative is 3x^2.
- Over the variable x, we have to multiply by dz/dx.

3. Repeat this process for each term in the equation.

To use Wolfram Alpha to compute these partial derivatives, follow these steps:

1. Open a web browser and go to www.wolframalpha.com.
2. Enter "partial derivative of (3x^2z - x^2y^2 + 2z^3 + 3yz - 5) with respect to x" in the search bar.
3. Click "Submit" or press "Enter" to compute the result.
4. Wolfram Alpha will return the calculated partial derivative. To find dz/dy, replace "x" in the query with "y" and repeat the process.

By following these steps, you should be able to find the partial derivatives dz/dx and dz/dy using Wolfram Alpha.

for ∂/∂z, enter

http://www.wolframalpha.com/input/?i=d%2Fdz+%283x^2z-x^2y^2%2B2z^3%2B3yz-5%29