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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

3 e^{5 x} \frac{d y}{d x} = - 25 \frac{x}{y ^{2}}

\int 2 tan (θ) d θ

\int 4 sin^{3} (x co) s^{5} x d x

2 e^{2}

\frac{d}{d x} (sec^{2} (5 x) \cdot 5)

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