Final answer:
The derivative of the function f(u) = 4u is 4, as calculated using the power rule of differentiation.
Step-by-step explanation:
The student is asking to find the derivative of the function f(u) = 4u using the rules of differentiation. The power rule of differentiation states that the derivative of cu^n with respect to u is ncu^(n-1), where c is a constant and n is a real number. In this case, since the function is a linear function, the derivative of f(u) = 4u with respect to u is simply the coefficient of u, which is 4.
The derivation process goes like this: f(u) = 4u can be seen as f(u) = 4u^1. Using the power rule, we have f'(u) = 1*4u^(1-1) = 4u^0. Since u^0 is 1 for any u, the final derivative is f'(u) = 4