What is the derivative of ((e^x)/x) ?

The derivative of ((e^x)/x) is (e^xx-e^x)/(x^2)

What is the first derivative of ((e^x)/x) ?

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

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

\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}}

f (x) = e^{x 7 x + 6}

\frac{7}{2 s ^{2 + 8}}

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

\int \frac{x ^{2} + 12 x - 1}{x ^{3} - x} d x

\int \frac{- sin ( x ) tan ( x )}{1} d x

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