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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (2 x) = 2

\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}}

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

\frac{d}{d x} (e^{- x^{2} - 5 x})

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

\int x^{2} - 7 x + 6 d x

\frac{d}{d x} (2 \cdot sin (x) \cdot cos (x))

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

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