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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

h \to 0 lim (\frac{\frac{4}{9 + h} - \frac{4}{9}}{h})

\int (3 t + 3)^{2.2} d t

\int_{0}^{1} sin (3 π x) d x

y = 6 x - 11

\int (\frac{5}{x} + sec^{2} (x)) d x

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