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

The derivative of (e^{2x}-1/(1-e^{-2x)}) is (2e^{-2x}+2e^{2x}-4)/((1-e^{-2x))^2}

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

The first derivative of (e^{2x}-1/(1-e^{-2x)}) is (2e^{-2x}+2e^{2x}-4)/((1-e^{-2x))^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{2 e ^{- 2 x} + 2 e ^{2 x} - 4}{( 1 - e ^{- 2 x} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

2 e^{2 x} (1 - e^{- 2 x}) - 2 e^{- 2 x} (e^{2 x} - 1) : 2 e^{- 2 x} + 2 e^{2 x} - 4

= \frac{2 e ^{- 2 x} + 2 e ^{2 x} - 4}{( 1 - e ^{- 2 x} ) ^{2}}

\frac{d}{d x} ((x^{2} + 17) (x^{3} - 3 x + 1))

y^{^{''}} + 9 y = 9 x^{2} + 9 x + 11

x \frac{d y}{d x} + y ln (x) - y = y ln (y)

\frac{\partial}{\partial y} (\frac{1}{x ^{2} yz})

\frac{d y}{d t} - \frac{5}{t} y = t^{5}

What is the derivative of (e^{2x}-1/(1-e^{-2x)}) ?
The derivative of (e^{2x}-1/(1-e^{-2x)}) is (2e^{-2x}+2e^{2x}-4)/((1-e^{-2x))^2}
What is the first derivative of (e^{2x}-1/(1-e^{-2x)}) ?
The first derivative of (e^{2x}-1/(1-e^{-2x)}) is (2e^{-2x}+2e^{2x}-4)/((1-e^{-2x))^2}