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Popular >

derivative of x/((x^2-1))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

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

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

Popular Examples

(\partial)/(\partial y)(ln(x/(x^2+y^2)))

\frac{\partial}{\partial y} (ln (\frac{x}{x ^{2} + y ^{2}}))

integral of t^3sqrt(1+t^2)

\int t^{3} 1 + t^{2} d t

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\int \frac{x}{2 x + 1} d x

Frequently Asked Questions (FAQ)

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