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Popular Calculus >

Find the Derivative - d/dx x/(x+1)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

1 \cdot (x + 1) - 1 \cdot x = 1

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

Graph

Popular Examples

Find the Antiderivative -1/u integral

\frac{- 1}{u}

Find dy/dx y=2x

\frac{d y}{d x} y = 2 x

Find the Derivative - d/dx x^(1/2)derivative of

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

Find the Derivative - d/dx y=sin(x)

\frac{d}{d x} y = sin (x)

Find the 2nd Derivative f(x)=cos(2x)second derivative

f (x) = cos (2 x)

Frequently Asked Questions (FAQ)

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