Final answer:
To find the first partial derivatives of a function, differentiate the function with respect to each variable, treating the others as constants.
Step-by-step explanation:
To find the first partial derivatives of a function, we differentiate the function with respect to each variable, treating the other variables as constants. Let's take the example of a function f(x, y, z, t).
a) To find ∂f/∂x, we differentiate f with respect to x while treating y, z, and t as constants.
b) To find ∂f/∂y, we differentiate f with respect to y while treating x, z, and t as constants.
c) To find ∂f/∂z, we differentiate f with respect to z while treating x, y, and t as constants.
d) To find ∂f/∂t, we differentiate f with respect to t while treating x, y, and z as constants.