What is the derivative of Ce^{-x} ?

The derivative of Ce^{-x} is -e^{-x}C

What is the first derivative of Ce^{-x} ?

The first derivative of Ce^{-x} is -e^{-x}C

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\frac{d}{d x} (C e^{- x})

- e^{- x} C

Solution steps

\frac{d}{d x} (C e^{- x})

Treat

C

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= C \frac{d}{d x} (e^{- x})

Apply the chain rule:

e^{- x} \frac{d}{d x} (- x)

= e^{- x} \frac{d}{d x} (- x)

\frac{d}{d x} (- x) = - 1

= C e^{- x} (- 1)

Simplify

= - e^{- x} C

What is the derivative of Ce^{-x} ?
The derivative of Ce^{-x} is -e^{-x}C
What is the first derivative of Ce^{-x} ?
The first derivative of Ce^{-x} is -e^{-x}C