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Popular >

derivative of ((e^x-1)/x)

Solution

\frac{d}{d x} (\frac{( e ^{x} - 1 )}{x})

Solution

\frac{e ^{x} x - e ^{x} + 1}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{( e ^{x} - 1 )}{x})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

= \frac{e ^{x} x - e ^{x} + 1}{x ^{2}}

Graph

Popular Examples

y^{''}-y^'-2y=-2t+6t^2

y^{^{''}} - y^{^{'}} - 2 y = - 2 t + 6 t^{2}

derivative of e^{sin^2(x})

\frac{d}{d x} (e^{s i n^{2} (x)})

area y= 2/x ,y=8x,y= 1/2 x area

y = \frac{2}{x}, y = 8 x, y = \frac{1}{2} x

derivative of 3/(4(2x-5^8))

\frac{d}{d x} (\frac{3}{4 ( 2 x - 5 ) ^{8}})

limit as x approaches-infinity of (sqrt(x^2+8x))/(8x+1)

x \to - \infty lim (\frac{x ^{2} + 8 x}{8 x + 1})

Frequently Asked Questions (FAQ)

What is the derivative of ((e^x-1)/x) ?
The derivative of ((e^x-1)/x) is (e^xx-e^x+1)/(x^2)
What is the first derivative of ((e^x-1)/x) ?
The first derivative of ((e^x-1)/x) is (e^xx-e^x+1)/(x^2)