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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}}

Popular Examples

derivative of 7/(3x+4)derivative of

\frac{7}{3 x + 4}

t y^{^{'}} + 4 y = 0

integral of 1/(y^2+3)

\int \frac{1}{y ^{2} + 3} d y

integral from-1 to 1 of (6x)/((x+4)^2)

\int_{- 1}^{1} \frac{6 x}{( x + 4 ) ^{2}} d x

sum from n=0 to infinity of n(z-1)^{n-1}

n = 0 \sum \infty n (z - 1)^{n - 1}

Frequently Asked Questions (FAQ)

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)