Question

Find the first partial derivatives of the function u = 2xy/z?

Answer 1

To find the first partial derivatives of the function u = 2xy/z, we calculate separately concerning x, y, and z, resulting in u_x = 2y/z, u_y = 2x/z, and u_z = -2xy/z^2.

Step-by-step explanation:

The question asks us to find the first partial derivatives of the function u = 2xy/z. Partial derivatives are used to show how a function changes as only one of the variables changes while the others are held constant. To find the first partial derivatives concerning x, y, and z, we treat the other variables as constants when differentiating concerning each one.

• The partial derivative of u concerning x is denoted as UX and is computed as:

ux = (2y/z)

• The partial derivative of u concerning y is denoted as uy and is computed as:

uy = (2x/z)

• The partial derivative of u concerning z is denoted as uz and is computed as:

uz = -2xy/z2