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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

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