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}}

\int \frac{7}{x ^{2} ( x ^{2} + 25 )} d x

f (x) = e^{- 2 x^{2}}

\frac{d y}{d x} + 20 = 24

\frac{\partial}{\partial x} (e^{x} + 1)

\int (z) d z

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)