find the derivative of ( f(x) ).\n\n( f(x)=e^{-3 x} )\n\n( f^{prime}(x)= )
find the derivative of ( f(x) ).\n\n( f(x)=e^{-3 x} )\n\n( f^{prime}(x)= )
Answer
Explanation:
Step1: Apply the chain rule
Let (u = -3x), then (f(x)=e^{u}). The chain rule states (\frac{df}{dx}=\frac{df}{du}\cdot\frac{du}{dx}). For (y = e^{u}), (\frac{dy}{du}=e^{u}). For (u=-3x), (\frac{du}{dx}=-3).
Step2: Substitute back
(f^{\prime}(x)=e^{u}\cdot(-3)). Substituting (u = -3x) back in, we get (f^{\prime}(x)=-3e^{-3x}).
Answer:
(-3e^{-3x})