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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x}{sin ^{2} ( 2 x ^{2} )} d x

\int (sin (x) - 7 cos (x)) d x

\int 2 ∣ x ∣ d x

\int \frac{e ^{x}}{e ^{2 x} + 9} d x

\int 7 sin^{4} (x co) s^{2} x d x

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