find the derivative of $f(x)$. $f(x)=e^{-5x}+e^{4x}$ $f(x)=$ submit

Explanation:

Step1: Differentiate (e^{-5x})

Use the chain rule ((e^{u})^\prime = e^{u}\cdot u^\prime). Let (u = -5x), then (u^\prime=-5). So ((e^{-5x})^\prime=e^{-5x}\cdot(-5)=-5e^{-5x}).

Step2: Differentiate (e^{4x})

Use the chain rule. Let (u = 4x), then (u^\prime = 4). So ((e^{4x})^\prime=e^{4x}\cdot4 = 4e^{4x}).

Step3: Find (f^\prime(x))

Since (f(x)=e^{-5x}+e^{4x}), then (f^\prime(x)=(e^{-5x})^\prime+(e^{4x})^\prime). Substitute the results from Step1 and Step2: (f^\prime(x)=-5e^{-5x}+4e^{4x}).

Answer:

(-5e^{-5x}+4e^{4x})