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

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

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

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

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derivative of

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

\frac{x ^{2} - 2}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

= \frac{x ^{2} - 2}{x ^{2}}

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

\int 2 t e^{- s t} d t

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

\int x^{2} e^{8 x} d x

\int_{0}^{6} \frac{1}{x ^{2} - 36} d x

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