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

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

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

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

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

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

Solution steps

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

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

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

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

Expand

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

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

\int 1 - 64 x^{2} d x

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

\int \frac{x - 1}{x ^{2} - 2 x} d x

\frac{d}{d t} (2)

\int x + x e^{x} d x

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