What is the derivative of (4x^2-7x+5)/(2x+1) ?

The derivative of (4x^2-7x+5)/(2x+1) is (8x^2+8x-17)/((2x+1)^2)

What is the first derivative of (4x^2-7x+5)/(2x+1) ?

The first derivative of (4x^2-7x+5)/(2x+1) is (8x^2+8x-17)/((2x+1)^2)

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derivative of

\frac{4 x ^{2} - 7 x + 5}{2 x + 1}

\frac{8 x ^{2} + 8 x - 17}{( 2 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{2} - 7 x + 5}{2 x + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} - 7 x + 5 ) ( 2 x + 1 ) - \frac{d}{d x} ( 2 x + 1 ) ( 4 x ^{2} - 7 x + 5 )}{( 2 x + 1 ) ^{2}}

\frac{d}{d x} (4 x^{2} - 7 x + 5) = 8 x - 7

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

= \frac{( 8 x - 7 ) ( 2 x + 1 ) - 2 ( 4 x ^{2} - 7 x + 5 )}{( 2 x + 1 ) ^{2}}

Expand

(8 x - 7) (2 x + 1) - 2 (4 x^{2} - 7 x + 5) : 8 x^{2} + 8 x - 17

= \frac{8 x ^{2} + 8 x - 17}{( 2 x + 1 ) ^{2}}

\int x^{2} - 5 x + 4 d x

n = 0 \sum \infty \frac{1}{10 0 ^{n}}

x \to 2 lim (x^{2} + 7 x - 5)

\int \frac{1 + ln ^{3} ( x )}{x} d x

\frac{d v}{d t} = - 2 v

What is the derivative of (4x^2-7x+5)/(2x+1) ?
The derivative of (4x^2-7x+5)/(2x+1) is (8x^2+8x-17)/((2x+1)^2)
What is the first derivative of (4x^2-7x+5)/(2x+1) ?
The first derivative of (4x^2-7x+5)/(2x+1) is (8x^2+8x-17)/((2x+1)^2)