en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ((e^{-x})/x)

Solution

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

Solution

\frac{- e ^{- x} x - e ^{- x}}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{- x} ) x - \frac{d x}{d x} e ^{- x}}{x ^{2}}

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

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

= \frac{( - e ^{- x} ) x - 1 \cdot e ^{- x}}{x ^{2}}

Simplify

= \frac{- e ^{- x} x - e ^{- x}}{x ^{2}}

Popular Examples

derivative of f(x)=(x-2)/(x^2-2x-3)derivative of

f (x) = \frac{x - 2}{x ^{2} - 2 x - 3}

tangent of f(x)=-3/2 x^2+3x+3 tangent of

f (x) = - \frac{3}{2} x^{2} + 3 x + 3

derivative of (e^x-2)^{1/2}derivative of

(e^{x} - 2)^{\frac{1}{2}}

integral of (xsin(2x))

\int (x sin (2 x)) d x

integral of sin(9x)cos(3x)

\int sin (9 x) cos (3 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of ((e^{-x})/x) ?
The derivative of ((e^{-x})/x) is (-e^{-x}x-e^{-x})/(x^2)
What is the first derivative of ((e^{-x})/x) ?
The first derivative of ((e^{-x})/x) is (-e^{-x}x-e^{-x})/(x^2)