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Popular >

derivative of x/(x+1)

Solution

derivative of

\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}}

Popular Examples

derivative of (1/(y^2)-7/(y^4))(y-3y^3)derivative of

(\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y - 3 y^{3})

(\partial)/(\partial y)(sin(x+2y+3z))

\frac{\partial}{\partial y} (sin (x + 2 y + 3 z))

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\int 2 cos^{3} (3 x) d x

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\int_{0}^{\frac{π}{2}} 28 x^{2} sin (x) d x

derivative of sqrt(1-x^3)

\frac{d}{d x} (1 - x^{3})

Frequently Asked Questions (FAQ)

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