What is the derivative of (3x-8/(x^2-1)) ?

The derivative of (3x-8/(x^2-1)) is (-3x^2+16x-3)/((x^2-1)^2)

What is the first derivative of (3x-8/(x^2-1)) ?

The first derivative of (3x-8/(x^2-1)) is (-3x^2+16x-3)/((x^2-1)^2)

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\frac{d}{d x} (\frac{3 x - 8}{x ^{2} - 1})

\frac{- 3 x ^{2} + 16 x - 3}{( x ^{2} - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x - 8}{x ^{2} - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x - 8 ) ( x ^{2} - 1 ) - \frac{d}{d x} ( x ^{2} - 1 ) ( 3 x - 8 )}{( x ^{2} - 1 ) ^{2}}

\frac{d}{d x} (3 x - 8) = 3

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

= \frac{3 ( x ^{2} - 1 ) - 2 x ( 3 x - 8 )}{( x ^{2} - 1 ) ^{2}}

Expand

3 (x^{2} - 1) - 2 x (3 x - 8) : - 3 x^{2} + 16 x - 3

= \frac{- 3 x ^{2} + 16 x - 3}{( x ^{2} - 1 ) ^{2}}

y^{^{'}} + \frac{3 y}{x} = \frac{3}{x}

y = \frac{9}{x ^{- 6}}

{\frac{s}{( s - 2 ) ( s - 3 ) ( s - 6 )}}

\frac{d}{d x} ((x + a) e^{3 x} + b)

4 x^{- 3} + 6 x^{- \frac{8}{3}}

What is the derivative of (3x-8/(x^2-1)) ?
The derivative of (3x-8/(x^2-1)) is (-3x^2+16x-3)/((x^2-1)^2)
What is the first derivative of (3x-8/(x^2-1)) ?
The first derivative of (3x-8/(x^2-1)) is (-3x^2+16x-3)/((x^2-1)^2)