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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{1 + x}{1 + e ^{x}}

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

Solution steps

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

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

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

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

Simplify

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

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

x = 8 y^{2}, x = 20 + 3 y^{2}

\frac{d}{d x} ((x^{2} + 5 x + 2)^{7})

\int x^{3} 64 - x^{2} d x

\int x 81 + x^{2} d x

y = 2 x, y = 12 - x, y = 4 - x

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