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

The derivative of (x^2/((x+1)^2)) is (2x)/((x+1)^3)

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (3 x e^{- 3 x y})

\int 5 (2 x - 1)^{4} d x

x \to 0 lim (3 arctan (e^{x}))

\int (a - x)^{2} d x

\int \frac{- 8 x ^{4} + 3 x ^{2} + 9}{3 x ^{3}} d x

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