Question

Find the derivative of AC = 30/q + 15 - 5q

Answer 1

To find the derivative of AC = 30/q + 15 - 5q with respect to q, we need to use the rules of differentiation.

Let's break down the given function into its individual terms:

AC = 30/q + 15 - 5q
AC = 30q^(-1) + 15 - 5q

Now, let's find the derivative of each term:

d/dq [30q^(-1)] = -30q^(-2) = -30/q^2
d/dq [15] = 0
d/dq [-5q] = -5

Now, we sum these derivatives to get the final derivative of AC:

d/dq [30/q + 15 - 5q] = -30/q^2 - 5

Therefore, the derivative of AC = 30/q + 15 - 5q is -30/q^2 - 5.