What is the derivative of c_{1}e^{-4x} ?

The derivative of c_{1}e^{-4x} is -4c_{1}e^{-4x}

What is the first derivative of c_{1}e^{-4x} ?

The first derivative of c_{1}e^{-4x} is -4c_{1}e^{-4x}

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\frac{d}{d x} (c_{1} e^{- 4 x})

- 4 c_{1} e^{- 4 x}

Solution steps

\frac{d}{d x} (c_{1} e^{- 4 x})

Take the constant out:

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

= c_{1} \frac{d}{d x} (e^{- 4 x})

Apply the chain rule:

e^{- 4 x} \frac{d}{d x} (- 4 x)

= e^{- 4 x} \frac{d}{d x} (- 4 x)

\frac{d}{d x} (- 4 x) = - 4

= c_{1} e^{- 4 x} (- 4)

Simplify

= - 4 c_{1} e^{- 4 x}

What is the derivative of c_{1}e^{-4x} ?
The derivative of c_{1}e^{-4x} is -4c_{1}e^{-4x}
What is the first derivative of c_{1}e^{-4x} ?
The first derivative of c_{1}e^{-4x} is -4c_{1}e^{-4x}