Question

find f(x). f(x)=3e - 9x f(x)=□

Explanation:

Step1: Recall derivative rules

The derivative of a constant - multiple of a function is the constant times the derivative of the function, i.e., \((cf(x))'=cf'(x)\), and the derivative of \(e^{ax}\) with respect to \(x\) is \(ae^{ax}\). Here \(c = 3\) and \(a=-9\) for the function \(y = 3e^{-9x}\).

Step2: Apply the rules

\(f(x)=3e^{-9x}\), so \(f'(x)=3\times(- 9)e^{-9x}\)

Answer:

\(-27e^{-9x}\)