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

The derivative of (ax-b/(x^2-1)) is (-ax^2+2bx-a)/((x^2-1)^2)

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

The first derivative of (ax-b/(x^2-1)) is (-ax^2+2bx-a)/((x^2-1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (a x - b) = a

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

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

Expand

a (x^{2} - 1) - 2 x (a x - b) : - a x^{2} + 2 b x - a

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

\int_{0}^{4} (4 - t) t d t

f (x) = x - \frac{4}{x}, at 0

2 y^{^{''}} + 4 y^{^{'}} = 0

y^{^{'}} + 2 y = 2

5 x^{3} lo g_{3} (x)

What is the derivative of (ax-b/(x^2-1)) ?
The derivative of (ax-b/(x^2-1)) is (-ax^2+2bx-a)/((x^2-1)^2)
What is the first derivative of (ax-b/(x^2-1)) ?
The first derivative of (ax-b/(x^2-1)) is (-ax^2+2bx-a)/((x^2-1)^2)