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

The derivative of (x^2)/((e^x-1)^2) is (2x(-e^xx+e^x-1))/((e^x-1)^3)

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

The first derivative of (x^2)/((e^x-1)^2) is (2x(-e^xx+e^x-1))/((e^x-1)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

\frac{2 x ( - e ^{x} x + e ^{x} - 1 )}{( e ^{x} - 1 ) ^{3}}

Solution steps

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

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

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

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

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

Simplify

\frac{2 x ( e ^{x} - 1 ) ^{2} - 2 ( e ^{x} - 1 ) e ^{x} x ^{2}}{( ( e ^{x} - 1 ) ^{2} ) ^{2}} : \frac{2 x ( - e ^{x} x + e ^{x} - 1 )}{( e ^{x} - 1 ) ^{3}}

= \frac{2 x ( - e ^{x} x + e ^{x} - 1 )}{( e ^{x} - 1 ) ^{3}}

What is the derivative of (x^2)/((e^x-1)^2) ?
The derivative of (x^2)/((e^x-1)^2) is (2x(-e^xx+e^x-1))/((e^x-1)^3)
What is the first derivative of (x^2)/((e^x-1)^2) ?
The first derivative of (x^2)/((e^x-1)^2) is (2x(-e^xx+e^x-1))/((e^x-1)^3)