What is the derivative of f(x)=(e^x)/(5-2x) ?

The derivative of f(x)=(e^x)/(5-2x) is (-2e^xx+7e^x)/((5-2x)^2)

What is the first derivative of f(x)=(e^x)/(5-2x) ?

The first derivative of f(x)=(e^x)/(5-2x) is (-2e^xx+7e^x)/((5-2x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = \frac{e ^{x}}{5 - 2 x}

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

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{5 - 2 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 5 - 2 x ) - \frac{d}{d x} ( 5 - 2 x ) e ^{x}}{( 5 - 2 x ) ^{2}}

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

\frac{d}{d x} (5 - 2 x) = - 2

= \frac{e ^{x} ( 5 - 2 x ) - ( - 2 ) e ^{x}}{( 5 - 2 x ) ^{2}}

Simplify

\frac{e ^{x} ( 5 - 2 x ) - ( - 2 ) e ^{x}}{( 5 - 2 x ) ^{2}} : \frac{- 2 e ^{x} x + 7 e ^{x}}{( 5 - 2 x ) ^{2}}

= \frac{- 2 e ^{x} x + 7 e ^{x}}{( 5 - 2 x ) ^{2}}

What is the derivative of f(x)=(e^x)/(5-2x) ?
The derivative of f(x)=(e^x)/(5-2x) is (-2e^xx+7e^x)/((5-2x)^2)
What is the first derivative of f(x)=(e^x)/(5-2x) ?
The first derivative of f(x)=(e^x)/(5-2x) is (-2e^xx+7e^x)/((5-2x)^2)