What is the derivative of x/(5+x) ?

The derivative of x/(5+x) is 5/((5+x)^2)

What is the first derivative of x/(5+x) ?

The first derivative of x/(5+x) is 5/((5+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{x}{5 + x})

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

Solution steps

\frac{d}{d x} (\frac{x}{5 + x})

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (5 + x) = 1

= \frac{1 \cdot ( 5 + x ) - 1 \cdot x}{( 5 + x ) ^{2}}

Simplify

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

What is the derivative of x/(5+x) ?
The derivative of x/(5+x) is 5/((5+x)^2)
What is the first derivative of x/(5+x) ?
The first derivative of x/(5+x) is 5/((5+x)^2)