Step 1 :The question is asking for the derivative of the function \((-5x-9)^{15}+C\). The derivative of a function gives us the rate of change of the function at any given point, which is what \(f(x)\) is in this case.
Step 2 :We can use the power rule for differentiation, which states that the derivative of \(x^n\) is \(nx^{n-1}\). We also know that the derivative of a constant is zero.
Step 3 :So, the derivative of \((-5x-9)^{15}\) is \(-75(-5x - 9)^{14}\).
Step 4 :Therefore, the final answer is \(f(x) = \boxed{-75(-5x - 9)^{14}}\).