What is the derivative of (e^x)/(e^x+7) ?

The derivative of (e^x)/(e^x+7) is (7e^x)/((e^x+7)^2)

What is the first derivative of (e^x)/(e^x+7) ?

The first derivative of (e^x)/(e^x+7) is (7e^x)/((e^x+7)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{e ^{x}}{e ^{x} + 7}

\frac{7 e ^{x}}{( e ^{x} + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{e ^{x} + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( e ^{x} + 7 ) - \frac{d}{d x} ( e ^{x} + 7 ) e ^{x}}{( e ^{x} + 7 ) ^{2}}

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

\frac{d}{d x} (e^{x} + 7) = e^{x}

= \frac{e ^{x} ( e ^{x} + 7 ) - e ^{x} e ^{x}}{( e ^{x} + 7 ) ^{2}}

Simplify

\frac{e ^{x} ( e ^{x} + 7 ) - e ^{x} e ^{x}}{( e ^{x} + 7 ) ^{2}} : \frac{7 e ^{x}}{( e ^{x} + 7 ) ^{2}}

= \frac{7 e ^{x}}{( e ^{x} + 7 ) ^{2}}

\frac{s e ^{- 3 s}}{( s - 4 ) ^{3}}

\frac{d}{d x} (sin (13 x))

\frac{\partial}{\partial h} (\frac{1}{3} π r^{2} h)

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

f (t) = t^{2} + 4 t

What is the derivative of (e^x)/(e^x+7) ?
The derivative of (e^x)/(e^x+7) is (7e^x)/((e^x+7)^2)
What is the first derivative of (e^x)/(e^x+7) ?
The first derivative of (e^x)/(e^x+7) is (7e^x)/((e^x+7)^2)