What is the derivative of (x^2-5x)/(x+1) ?

The derivative of (x^2-5x)/(x+1) is (x^2+2x-5)/((x+1)^2)

What is the first derivative of (x^2-5x)/(x+1) ?

The first derivative of (x^2-5x)/(x+1) is (x^2+2x-5)/((x+1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{x ^{2} - 5 x}{x + 1}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

What is the derivative of (x^2-5x)/(x+1) ?
The derivative of (x^2-5x)/(x+1) is (x^2+2x-5)/((x+1)^2)
What is the first derivative of (x^2-5x)/(x+1) ?
The first derivative of (x^2-5x)/(x+1) is (x^2+2x-5)/((x+1)^2)