What is the derivative of f(x)=(4x)/(x+1) ?

The derivative of f(x)=(4x)/(x+1) is 4/((x+1)^2)

What is the first derivative of f(x)=(4x)/(x+1) ?

The first derivative of f(x)=(4x)/(x+1) is 4/((x+1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{4 x}{x + 1}

\frac{4}{( x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x}{x + 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (\frac{x}{x + 1})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d x}{d x} ( x + 1 ) - \frac{d}{d x} ( x + 1 ) x}{( x + 1 ) ^{2}}

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

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

= 4 \cdot \frac{1 \cdot ( x + 1 ) - 1 \cdot x}{( x + 1 ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot ( x + 1 ) - 1 \cdot x}{( x + 1 ) ^{2}} : \frac{4}{( x + 1 ) ^{2}}

= \frac{4}{( x + 1 ) ^{2}}

\int \frac{x ^{5}}{( 8 - x ^{6} ) ^{2}} d x

\int \frac{2}{5 x - 8} d x

\int \frac{( x ^{3} - 4 x - 10 )}{( x ^{2} - x - 6 )} d x

\int \frac{5}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

\frac{d}{d x} (- \frac{7}{x ^{4}})

What is the derivative of f(x)=(4x)/(x+1) ?
The derivative of f(x)=(4x)/(x+1) is 4/((x+1)^2)
What is the first derivative of f(x)=(4x)/(x+1) ?
The first derivative of f(x)=(4x)/(x+1) is 4/((x+1)^2)