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)

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\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}}

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

y = 6 x - 11

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

x \to 2 lim (3.5 + 5.6)

x \to 2 - lim (\frac{2 - ∣ x ∣}{2 + 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)