What is the derivative of-4.5xe^{-x/(3.8}) ?

The derivative of-4.5xe^{-x/(3.8}) is -4.5(e^{-x/(3.8)}-0.26315…e^{-x/(3.8)}x)

What is the first derivative of-4.5xe^{-x/(3.8}) ?

The first derivative of-4.5xe^{-x/(3.8}) is -4.5(e^{-x/(3.8)}-0.26315…e^{-x/(3.8)}x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (- 4.5 x e^{- \frac{x}{3.8}})

- 4.5 (e^{- \frac{x}{3.8}} - 0.26315 \dots e^{- \frac{x}{3.8}} x)

Solution steps

\frac{d}{d x} (- 4.5 x e^{- \frac{x}{3.8}})

Take the constant out:

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

= - 4.5 \frac{d}{d x} (x e^{- \frac{x}{3.8}})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{- \frac{x}{3.8}}

= - 4.5 (\frac{d x}{d x} e^{- \frac{x}{3.8}} + \frac{d}{d x} (e^{- \frac{x}{3.8}}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{- \frac{x}{3.8}}) = - 0.26315 \dots e^{- \frac{x}{3.8}}

= - 4.5 (1 \cdot e^{- \frac{x}{3.8}} + (- 0.26315 \dots e^{- \frac{x}{3.8}}) x)

Simplify

= - 4.5 (e^{- \frac{x}{3.8}} - 0.26315 \dots e^{- \frac{x}{3.8}} x)

What is the derivative of-4.5xe^{-x/(3.8}) ?
The derivative of-4.5xe^{-x/(3.8}) is -4.5(e^{-x/(3.8)}-0.26315…e^{-x/(3.8)}x)
What is the first derivative of-4.5xe^{-x/(3.8}) ?
The first derivative of-4.5xe^{-x/(3.8}) is -4.5(e^{-x/(3.8)}-0.26315…e^{-x/(3.8)}x)