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

The derivative of ((x+1(2x-3))/(2x+3)) is (4x^2+12x+3)/((2x+3)^2)

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

The first derivative of ((x+1(2x-3))/(2x+3)) is (4x^2+12x+3)/((2x+3)^2)

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

\frac{4 x ^{2} + 12 x + 3}{( 2 x + 3 ) ^{2}}

Solution steps

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

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

\frac{d}{d x} ((x + 1) (2 x - 3)) = 4 x - 1

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

= \frac{( 4 x - 1 ) ( 2 x + 3 ) - 2 ( x + 1 ) ( 2 x - 3 )}{( 2 x + 3 ) ^{2}}

Expand

(4 x - 1) (2 x + 3) - 2 (x + 1) (2 x - 3) : 4 x^{2} + 12 x + 3

= \frac{4 x ^{2} + 12 x + 3}{( 2 x + 3 ) ^{2}}

What is the derivative of ((x+1(2x-3))/(2x+3)) ?
The derivative of ((x+1(2x-3))/(2x+3)) is (4x^2+12x+3)/((2x+3)^2)
What is the first derivative of ((x+1(2x-3))/(2x+3)) ?
The first derivative of ((x+1(2x-3))/(2x+3)) is (4x^2+12x+3)/((2x+3)^2)