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Popular Calculus >

derivative of x(x+1)^{-1}

Solution

derivative of

x (x + 1)^{- 1}

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (x + 1)^{- 1}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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