en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of-xe^{-x}

Solution

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

Solution

- e^{- x} + e^{- x} x

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= - e^{- x} + e^{- x} x

Popular Examples

derivative of 32x

\frac{d}{d x} (32 x)

limit as x approaches 0+of 10xln(x)

x \to 0 + lim (10 x ln (x))

limit as x approaches 2-of (-3)/(x^2-4)

x \to 2 - lim (\frac{- 3}{x ^{2} - 4})

laplacetransform 5e-3(t-2)laplace transform

5 e - 3 (t - 2)

(\partial)/(\partial x)(3x^2y+2xy^2)

\frac{\partial}{\partial x} (3 x^{2} y + 2 x y^{2})

Frequently Asked Questions (FAQ)

What is the derivative of-xe^{-x} ?
The derivative of-xe^{-x} is -e^{-x}+e^{-x}x
What is the first derivative of-xe^{-x} ?
The first derivative of-xe^{-x} is -e^{-x}+e^{-x}x