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

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

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

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

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

2 x - 1

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 2 x - 1 + 0

Simplify

= 2 x - 1

x \to 0 lim (\frac{( a ^{x} - 1 )}{x})

\int_{1}^{5} (x + 1)^{2} d x

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

\frac{\partial}{\partial x} (2 x^{y})

\frac{d x}{d t} = x - 11

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