en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 3xe^{-3x}

Solution

\frac{d}{d x} (3 x e^{- 3 x})

Solution

3 (e^{- 3 x} - 3 e^{- 3 x} x)

Solution steps

\frac{d}{d x} (3 x e^{- 3 x})

Take the constant out:

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

= 3 \frac{d}{d x} (x e^{- 3 x})

Apply the Product Rule:

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

f = x, g = e^{- 3 x}

= 3 (\frac{d x}{d x} e^{- 3 x} + \frac{d}{d x} (e^{- 3 x}) x)

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

\frac{d}{d x} (e^{- 3 x}) = - 3 e^{- 3 x}

= 3 (1 \cdot e^{- 3 x} + (- 3 e^{- 3 x}) x)

Simplify

= 3 (e^{- 3 x} - 3 e^{- 3 x} x)

Popular Examples

(\partial)/(\partial x)(2cos(4x))

\frac{\partial}{\partial x} (2 cos (4 x))

taylor e^{e^t}taylor

e^{e^{t}}

integral of 5sec^2(5x)tan^5(5x)

\int 5 sec^{2} (5 x) tan^{5} (5 x) d x

derivative of ((x+1)/2)

\frac{d}{d x} (\frac{( x + 1 )}{2})

d/(dt)(a(1-cos(t)))

\frac{d}{d t} (a (1 - cos (t)))

Frequently Asked Questions (FAQ)

What is the derivative of 3xe^{-3x} ?
The derivative of 3xe^{-3x} is 3(e^{-3x}-3e^{-3x}x)
What is the first derivative of 3xe^{-3x} ?
The first derivative of 3xe^{-3x} is 3(e^{-3x}-3e^{-3x}x)