Question

find the derivative of ( f(x) ).

( f(x)=-4 e^{-3 x}-3 e^{-4 x} )

( f^{prime}(x)= )

Explanation:

Step1: Apply derivative rules

The derivative of $e^{ax}$ is $ae^{ax}$ (by chain rule).

Step2: Differentiate term - by - term

For $-4e^{-3x}$:
Using the rule, the derivative is $-4\times(-3)e^{-3x}=12e^{-3x}$.
For $-3e^{-4x}$:
Using the rule, the derivative is $-3\times(-4)e^{-4x}=12e^{-4x}$.

Step3: Combine results

$f^{\prime}(x)=12e^{-3x}+12e^{-4x}$.

Answer:

$12e^{-3x}+12e^{-4x}$