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

The derivative of (x^2-3x+2)/(2x+1) is (2x^2+2x-7)/((2x+1)^2)

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

The first derivative of (x^2-3x+2)/(2x+1) is (2x^2+2x-7)/((2x+1)^2)

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derivative of

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

\frac{2 x ^{2} + 2 x - 7}{( 2 x + 1 ) ^{2}}

Solution steps

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

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

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

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

Expand

(2 x - 3) (2 x + 1) - 2 (x^{2} - 3 x + 2) : 2 x^{2} + 2 x - 7

= \frac{2 x ^{2} + 2 x - 7}{( 2 x + 1 ) ^{2}}

What is the derivative of (x^2-3x+2)/(2x+1) ?
The derivative of (x^2-3x+2)/(2x+1) is (2x^2+2x-7)/((2x+1)^2)
What is the first derivative of (x^2-3x+2)/(2x+1) ?
The first derivative of (x^2-3x+2)/(2x+1) is (2x^2+2x-7)/((2x+1)^2)