What is the derivative of x/(e^x-1) ?

The derivative of x/(e^x-1) is (e^x-1-e^xx)/((e^x-1)^2)

What is the first derivative of x/(e^x-1) ?

The first derivative of x/(e^x-1) is (e^x-1-e^xx)/((e^x-1)^2)

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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