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

The derivative of ((x+1(2x-7))/(2x+1)) is (4x^2+4x+9)/((2x+1)^2)

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

The first derivative of ((x+1(2x-7))/(2x+1)) is (4x^2+4x+9)/((2x+1)^2)

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

\frac{4 x ^{2} + 4 x + 9}{( 2 x + 1 ) ^{2}}

Solution steps

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

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

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

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

Expand

(4 x - 5) (2 x + 1) - 2 (x + 1) (2 x - 7) : 4 x^{2} + 4 x + 9

= \frac{4 x ^{2} + 4 x + 9}{( 2 x + 1 ) ^{2}}

What is the derivative of ((x+1(2x-7))/(2x+1)) ?
The derivative of ((x+1(2x-7))/(2x+1)) is (4x^2+4x+9)/((2x+1)^2)
What is the first derivative of ((x+1(2x-7))/(2x+1)) ?
The first derivative of ((x+1(2x-7))/(2x+1)) is (4x^2+4x+9)/((2x+1)^2)