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

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

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

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

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

\frac{- x ^{2} + 6 x - 1}{( x ^{2} - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{- x ^{2} + 6 x - 1}{( x ^{2} - 1 ) ^{2}}

\frac{d}{d x} ((x + y)^{2})

\int cos (\frac{x}{5}) d x

\int x^{2} + 2 d x

h^{2} (2 t)

y = 3 x^{2} (x - 3)^{3}

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