find the derivative of ( f(x) ).\n\n( f(x)=e^{-2 x} )\n\n( f^{prime}(x)= )
find the derivative of ( f(x) ).\n\n( f(x)=e^{-2 x} )\n\n( f^{prime}(x)= )
Answer
Explanation:
Step1: Apply the chain rule
Let (u = - 2x), then (f(x)=e^{u}). The chain rule states (\frac{df}{dx}=\frac{df}{du}\cdot\frac{du}{dx}). The derivative of (e^{u}) with respect to (u) is (e^{u}), and the derivative of (u=-2x) with respect to (x) is (-2).
Step2: Substitute back
Since (u = - 2x), (\frac{df}{dx}=e^{-2x}\cdot(-2))
Answer:
(-2e^{-2x})