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

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

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

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

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

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

Solution steps

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

Simplify

\frac{- x ^{2}}{x + 1} : - \frac{x ^{2}}{x + 1}

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

Take the constant out:

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

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

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

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

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

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

Simplify

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

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

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