Question

Find the first partial derivatives of the function. u = 6xy/z. ∂u/∂x = ?, ∂u/∂y = ?

Answer 1

The first partial derivatives of the function u = 6xy/z are ∂u/∂x = 6y/z and ∂u/∂y = 6x/z, treating other variables as constants while differentiating.

Step-by-step explanation:

Finding the First Partial Derivatives

To find the first partial derivatives ∂u/∂x and ∂u/∂y of the function u = 6xy/z, we will treat one variable as a constant while differentiating with respect to the other. For the partial derivative with respect to x, we treat y and z as constants:

∂u/∂x = ∂(6xy/z)/∂x = 6(z∂x/y∂z)/z = 6y/z

Similarly, for the partial derivative with respect to y, we treat x and z as constants:

∂u/∂y = ∂(6xy/z)/∂y = 6(x∂y/z∂x)/z = 6x/z

The first partial derivatives of the function are:

• ∂u/∂x = 6y/z
• ∂u/∂y = 6x/z