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Popular Calculus >

derivative of (x/(x+1)^2)

Solution

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

Solution

\frac{2 x}{( x + 1 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 \cdot \frac{x}{x + 1} \cdot \frac{1}{( x + 1 ) ^{2}} : \frac{2 x}{( x + 1 ) ^{3}}

= \frac{2 x}{( x + 1 ) ^{3}}

Graph

Popular Examples

derivative of e^{-6x}

d er i v a t i v e e^{- 6 x}

derivative of 7cos(x+3e^x)

\frac{d}{d x} (7 cos (x) + 3 e^{x})

derivative of y=sqrt(1+cot^2(x))

d er i v a t i v e y = 1 + cot^{2} (x)

derivative of e^{2x}+e^{3x}

\frac{d}{d x} (e^{2 x} + e^{3 x})

y^{^{'}} - 5 y = 10

Frequently Asked Questions (FAQ)

What is the derivative of (x/(x+1)^2) ?
The derivative of (x/(x+1)^2) is (2x)/((x+1)^3)
What is the first derivative of (x/(x+1)^2) ?
The first derivative of (x/(x+1)^2) is (2x)/((x+1)^3)