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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

Popular Examples

derivative of (2(x^2+3)/(3sqrt(x)))

\frac{d}{d x} (\frac{2 ( x ^{2} + 3 )}{3 x})

derivative of (2x^{3/2}/x)

\frac{d}{d x} (\frac{2 x ^{\frac{3}{2}}}{x})

sum from n=1 to infinity of (3^n)/(n^3)

n = 1 \sum \infty \frac{3 ^{n}}{n ^{3}}

integral of (sin(2x))/((1+cos(2x))^3)

\int \frac{sin ( 2 x )}{( 1 + cos ( 2 x ) ) ^{3}} d x

derivative of f(x)=(x^5)/5+1/(12x^3)derivative of

f (x) = \frac{x ^{5}}{5} + \frac{1}{12 x ^{3}}

Frequently Asked Questions (FAQ)

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