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

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

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

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

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derivative of

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

2 x

Solution steps

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

Simplify

\frac{x ^{3} + 2 x ^{2} + x + 2}{x + 2} : x^{2} + 1

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (1) = 0

= 2 x + 0

Simplify

= 2 x

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