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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}}

Graph

Popular Examples

integral from-1 to 1 of e^y-(y^2-9)

\int_{- 1}^{1} e^{y} - (y^{2} - 9) d y

(14-6y+e-3x)dx-2dy=0

(14 - 6 y + e - 3 x) d x - 2 d y = 0

integral from 0 to 6 of pi/8 (6-x)^2

\int_{0}^{6} \frac{π}{8} (6 - x)^{2} d x

integral of sin^4(xco)s^2x

\int sin^{4} (x co) s^{2} x d x

derivative of y=(cos(x))/(x^7)derivative of

y = \frac{cos ( x )}{x ^{7}}

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)