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

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

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

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

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

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

Solution steps

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

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

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

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

Expand

(2 x + 1) (x^{2} - x + 1) - (2 x - 1) (x^{2} + x + 1) : - 2 x^{2} + 2

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

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

x \to 0 lim (\frac{1}{2 x ^{3}})

y = \frac{4 x ^{2} + 6 x}{3 x ^{3} + 2}

x \to \infty lim ((\frac{( e ^{x} - e ^{- x} )}{( e ^{x} + e ^{- x} )}) + 4)

\int (5 cos (x) - 4, x) d x

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