What is the derivative of (e^x/(4+e^x)) ?

The derivative of (e^x/(4+e^x)) is (4e^x)/((4+e^x)^2)

What is the first derivative of (e^x/(4+e^x)) ?

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

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

Solution steps

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

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

\frac{d}{d x} (4 + e^{x}) = e^{x}

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

Simplify

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

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

\frac{d}{d x} (\frac{x ^{3} - 5 x ^{2} - 36 x}{x ^{2} + 4 x})

\frac{25}{x ( x ^{2} + 6 x + 25 )}

\frac{d x}{d t} = x - 12

\frac{d}{d x} (sin (\frac{1}{x}) \cdot x^{3})

cos (sin (tan (5 x)))

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