What is the derivative of (2x^2+4x)/((x+1)^2) ?

The derivative of (2x^2+4x)/((x+1)^2) is 4/((x+1)^3)

What is the first derivative of (2x^2+4x)/((x+1)^2) ?

The first derivative of (2x^2+4x)/((x+1)^2) is 4/((x+1)^3)

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derivative of

\frac{2 x ^{2} + 4 x}{( x + 1 ) ^{2}}

\frac{4}{( x + 1 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{2} + 4 x}{( x + 1 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x ^{2} + 4 x ) ( x + 1 ) ^{2} - \frac{d}{d x} ( ( x + 1 ) ^{2} ) ( 2 x ^{2} + 4 x )}{( ( x + 1 ) ^{2} ) ^{2}}

\frac{d}{d x} (2 x^{2} + 4 x) = 4 x + 4

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

= \frac{( 4 x + 4 ) ( x + 1 ) ^{2} - 2 ( x + 1 ) ( 2 x ^{2} + 4 x )}{( ( x + 1 ) ^{2} ) ^{2}}

Simplify

\frac{( 4 x + 4 ) ( x + 1 ) ^{2} - 2 ( x + 1 ) ( 2 x ^{2} + 4 x )}{( ( x + 1 ) ^{2} ) ^{2}} : \frac{4}{( x + 1 ) ^{3}}

= \frac{4}{( x + 1 ) ^{3}}

What is the derivative of (2x^2+4x)/((x+1)^2) ?
The derivative of (2x^2+4x)/((x+1)^2) is 4/((x+1)^3)
What is the first derivative of (2x^2+4x)/((x+1)^2) ?
The first derivative of (2x^2+4x)/((x+1)^2) is 4/((x+1)^3)