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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

x \to - 2 lim (f (x) x)

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

x \to 0 lim (x ln (x + x^{2}))

\int \frac{x ^{2} - 64}{x} d x

\frac{1 + 2 x}{3 - 4 x}

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