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Popular >

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

Solution

derivative of

f (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

integral of (cos(x^2))/x

\int \frac{cos ( x ^{2} )}{x} d x

derivative of (1/2)^{x-1}+3 derivative of

(\frac{1}{2})^{x - 1} + 3

limit as x approaches 1 of-log_{10}(x-1)

x \to 1 lim (- lo g_{10} (x - 1))

integral of (x^3)/(a^2-x^2)

\int \frac{x ^{3}}{a ^{2} - x ^{2}} d x

derivative of (t^5-3t^2)/(2t)derivative of

\frac{t ^{5} - 3 t ^{2}}{2 t}

Frequently Asked Questions (FAQ)

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