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Popular >

derivative of x/(sqrt(x)+1)

Solution

derivative of

\frac{x}{x + 1}

Solution

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

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

Simplify

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

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

Graph

Popular Examples

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\int x^{5} cos (y^{4}) d x

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Frequently Asked Questions (FAQ)

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