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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

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

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

Cancel

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

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

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