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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int cos (2 πn x) d x

n = 0 \sum \infty \frac{( x - 3 ) ^{n}}{n}

\frac{d}{d x} (\frac{1}{e ^{\frac{1}{x}}})

\frac{d}{d x} (2 x - 9)

x \to 0 lim (4^{x})

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