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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int x x^{2} - 1 d x

\int_{1}^{32} x^{- \frac{6}{5}} d x

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

\frac{d}{d x} (3 x (6 x - 5 x^{2}))

\frac{d}{d x} ((80 e^{- \frac{x}{10}}) - 40 x)

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