Final answer:
To find the first partial derivatives of the function u = xy/z, differentiate u with respect to x and treat y and z as constants. The derivative with respect to x is y/z. Then differentiate u with respect to y and treat x and z as constants. The derivative with respect to y is x/z.
Step-by-step explanation:
To find the first partial derivatives of the function u = xy/z, we need to find the derivative of u with respect to x and the derivative of u with respect to y while treating z as a constant.
To find the partial derivative of u with respect to x, we differentiate u with respect to x and treat y and z as constants. The derivative of xy/z with respect to x is (y/z).
To find the partial derivative of u with respect to y, we differentiate u with respect to y and treat x and z as constants. The derivative of xy/z with respect to y is (x/z).