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

The derivative of ((-x^2+2x+2))/((x+1)^4) is (2(x^2-4x-3))/((x+1)^5)

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

The first derivative of ((-x^2+2x+2))/((x+1)^4) is (2(x^2-4x-3))/((x+1)^5)

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derivative of

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

\frac{2 ( x ^{2} - 4 x - 3 )}{( x + 1 ) ^{5}}

Solution steps

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

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

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

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

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

Simplify

\frac{( - 2 x + 2 ) ( x + 1 ) ^{4} - 4 ( x + 1 ) ^{3} ( - x ^{2} + 2 x + 2 )}{( ( x + 1 ) ^{4} ) ^{2}} : \frac{2 ( x ^{2} - 4 x - 3 )}{( x + 1 ) ^{5}}

= \frac{2 ( x ^{2} - 4 x - 3 )}{( x + 1 ) ^{5}}

What is the derivative of ((-x^2+2x+2))/((x+1)^4) ?
The derivative of ((-x^2+2x+2))/((x+1)^4) is (2(x^2-4x-3))/((x+1)^5)
What is the first derivative of ((-x^2+2x+2))/((x+1)^4) ?
The first derivative of ((-x^2+2x+2))/((x+1)^4) is (2(x^2-4x-3))/((x+1)^5)