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Popular Calculus >

Find the Derivative - d/dx (e^x)/x

Solution

derivative of

\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

limit as x approaches infinity of ( square root of x+x^2)/(2x-x^2)

x \to \infty lim (\frac{x , x , ( x + x ^{2} )}{( 2 x - x ^{2} )})

Find the Derivative - d/dx y=7/x

\frac{d}{d x} y = \frac{7}{x}

Find the Derivative - d/dx 8/x derivative of

\frac{d}{d x} (\frac{8}{x})

Find the Derivative - d/dx tan(x/2)derivative of

\frac{d}{d x} (tan (\frac{x}{2}))

Find the Derivative - d/dx e^2 derivative of

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

Frequently Asked Questions (FAQ)

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