Let's say we are given g = f(x,y,z), and we wish to take the partial derivative of g with respect to x (i.e. ∂g/∂x).
This simply means that we will obtain the derivative of g with respect to x while treating the other variables (i.e. y and z) as though they were constants. We will solve #3 to demonstrate:
Solve for ∂g/∂x. We treat the variable y as though it were a constant. So...
The third term "disappeared" because, in this case, cy^2 is treated as a constant, and the derivative of a constant is 0.
Thus, we obtain:
Similarly, ∂g/∂y is: