Question

7. If f(x) = ae^-ax for a > 0, then f'(x) =

Answer 1

`f'(x)=-a^2e^(-ax)`

General Formulas and Concepts:

Calculus

• Chain Rule:
  `(d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)`

• Derivative:
  `(d)/(dx) [e^u]=e^u \cdot u'`

Explanation:

Step 1: Define

`f(x)=ae^(-ax)`

Step 2: Find Derivative

1. Derivative eˣ [Chain Rule]:
   `f'(x)=ae^(-ax) \cdot -a`
2. Condense/Simplify:
   `f'(x)=-a^2e^(-ax)`