Question

The question is in the photo

Answer 1

`f_z(x, y) = 12x^5 + 3y^4\\f_y(x, y) = 12xy^3 - 3y^2`

The given function is f(x, y) =
`2x^6 + 3xy^4 - y^3`. To find the partial derivatives of f, we treat y as a constant when taking the partial derivative with respect to x, and vice versa.

Finding
`f_z(x, y)`

When taking the partial derivative with respect to x, we treat y as a constant. Therefore, the partial derivative of f with respect to x is:

`f_z(x, y) = 12x^5 + 3y^4`

Finding
`f_y(x, y)`

When taking the partial derivative with respect to y, we treat x as a constant. Therefore, the partial derivative of f with respect to y is:

`f_y(x, y) = 12xy^3 - 3y^2`