What is the derivative of (e^x/(4-3e^x)) ?

The derivative of (e^x/(4-3e^x)) is (4e^x)/((4-3e^x)^2)

What is the first derivative of (e^x/(4-3e^x)) ?

The first derivative of (e^x/(4-3e^x)) is (4e^x)/((4-3e^x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{e ^{x}}{4 - 3 e ^{x}})

\frac{4 e ^{x}}{( 4 - 3 e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{4 - 3 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 - 3 e ^{x} ) - \frac{d}{d x} ( 4 - 3 e ^{x} ) e ^{x}}{( 4 - 3 e ^{x} ) ^{2}}

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

\frac{d}{d x} (4 - 3 e^{x}) = - 3 e^{x}

= \frac{e ^{x} ( 4 - 3 e ^{x} ) - ( - 3 e ^{x} ) e ^{x}}{( 4 - 3 e ^{x} ) ^{2}}

Simplify

\frac{e ^{x} ( 4 - 3 e ^{x} ) - ( - 3 e ^{x} ) e ^{x}}{( 4 - 3 e ^{x} ) ^{2}} : \frac{4 e ^{x}}{( 4 - 3 e ^{x} ) ^{2}}

= \frac{4 e ^{x}}{( 4 - 3 e ^{x} ) ^{2}}

What is the derivative of (e^x/(4-3e^x)) ?
The derivative of (e^x/(4-3e^x)) is (4e^x)/((4-3e^x)^2)
What is the first derivative of (e^x/(4-3e^x)) ?
The first derivative of (e^x/(4-3e^x)) is (4e^x)/((4-3e^x)^2)