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

The derivative of (2x-5)/(x^2-1) is (-2x^2+10x-2)/((x^2-1)^2)

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

The first derivative of (2x-5)/(x^2-1) is (-2x^2+10x-2)/((x^2-1)^2)

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derivative of

\frac{2 x - 5}{x ^{2} - 1}

\frac{- 2 x ^{2} + 10 x - 2}{( x ^{2} - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (2 x - 5) = 2

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

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

Expand

2 (x^{2} - 1) - 2 x (2 x - 5) : - 2 x^{2} + 10 x - 2

= \frac{- 2 x ^{2} + 10 x - 2}{( x ^{2} - 1 ) ^{2}}

x \to - 1 lim (arctan (x))

\frac{d}{d x} (arcsinh (\frac{2 x + 5}{23}))

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

- \frac{8}{x ^{2}} - \frac{8}{x}

What is the derivative of (2x-5)/(x^2-1) ?
The derivative of (2x-5)/(x^2-1) is (-2x^2+10x-2)/((x^2-1)^2)
What is the first derivative of (2x-5)/(x^2-1) ?
The first derivative of (2x-5)/(x^2-1) is (-2x^2+10x-2)/((x^2-1)^2)