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Popular >

derivative of (e^x-1)/x

Solution

derivative of

\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}}

Popular Examples

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\int tan^{8} (x) cos^{9} (x) d x

derivative of y=10^x derivative of

y = 1 0^{x}

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)