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

The derivative of ((x^2-1)/(2x-3)) is (2x^2-6x+2)/((2x-3)^2)

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

The first derivative of ((x^2-1)/(2x-3)) is (2x^2-6x+2)/((2x-3)^2)

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

\frac{2 x ^{2} - 6 x + 2}{( 2 x - 3 ) ^{2}}

Solution steps

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

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

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

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

Expand

2 x (2 x - 3) - 2 (x^{2} - 1) : 2 x^{2} - 6 x + 2

= \frac{2 x ^{2} - 6 x + 2}{( 2 x - 3 ) ^{2}}

x \to 1 + lim (∣ x ∣)

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

y = \frac{3}{2}, y = \frac{1}{1 - x ^{2}}

ln (\frac{e ^{2 x} ( x ^{2} + 3 )}{x + 2})

- x^{2} + 3 x - 2

What is the derivative of ((x^2-1)/(2x-3)) ?
The derivative of ((x^2-1)/(2x-3)) is (2x^2-6x+2)/((2x-3)^2)
What is the first derivative of ((x^2-1)/(2x-3)) ?
The first derivative of ((x^2-1)/(2x-3)) is (2x^2-6x+2)/((2x-3)^2)