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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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

ln (3 - 2 x)

\int (\frac{x ^{2} + 9}{x ^{3}}) d x

3 cos^{3} (5 x)

y^{^{'}} = \frac{2 x y - y ^{2}}{x ^{2}}

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