en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 16xe^{-x}

Solution

\frac{d}{d x} (16 x e^{- x})

Solution

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

Solution steps

\frac{d}{d x} (16 x e^{- x})

Take the constant out:

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

= 16 \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}

= 16 (\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}

= 16 (1 \cdot e^{- x} + (- e^{- x}) x)

Simplify

= 16 (e^{- x} - e^{- x} x)

Popular Examples

integral of-3x^{-4}

\int - 3 x^{- 4} d x

limit as x approaches 1+of sqrt(x^2-1)

x \to 1 + lim (x^{2} - 1)

integral from 0 to 1 of 2x(1-x)

\int_{0}^{1} 2 x (1 - x) d x

derivative of 2tan^3(x)derivative of

2 tan^{3} (x)

(\partial)/(\partial x)(6xy+5x^2)

\frac{\partial}{\partial x} (6 x y + 5 x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of 16xe^{-x} ?
The derivative of 16xe^{-x} is 16(e^{-x}-e^{-x}x)
What is the first derivative of 16xe^{-x} ?
The first derivative of 16xe^{-x} is 16(e^{-x}-e^{-x}x)