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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

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

\frac{d}{d x} (- 8 ln (x))

y = 7 x^{- 7}

(3 x + 2 y + 2 y^{2}) d x + (x + 2 x y) d y = 0

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