Question

Assume that 0 implicitly defines z as a differentiable function of x and y. What are the partial derivatives of z?

Answer 1

The partial derivative of z with respect to x is 2dx, and the partial derivative of z with respect to y is -2y.

Step-by-step explanation:

To find the partial derivatives of z, we differentiate the given function with respect to x and y separately while treating the other variable as a constant. Let's start with the partial derivative with respect to x:

∂z/∂x = 2dx - 0∂y²/∂x = 2dx

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

∂z/∂y = 0dx - 2y∂y/∂y = -2y