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

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

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

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

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

Solution steps

\frac{d}{d x} (\frac{1}{x ( x + 2 )})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d x} (x (x + 2)) = 2 x + 2

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

Simplify

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

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

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