Final answer:
To find the first partial derivatives of the function f(u,v,w), differentiate the function with respect to each variable individually, treating all other variables as constants during each differentiation.
Step-by-step explanation:
The question asks us to find the first partial derivatives of a function f(u,v,w) with respect to its variables u, v, and w. To find the partial derivative with respect to one variable, we treat the other variables as constants and differentiate accordingly. For example, the partial derivative of f with respect to u, denoted as f_u, would involve differentiating f with u being the variable and v and w being treated as constants. Similarly, f_v and f_w are found by differentiating with respect to v and w, respectively, treating all other variables as constants in each case.