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Popular >

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

Solution

derivative of

f (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

(d^2y)/(dx^2)-2(dy)/(dx)-8y=0

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 8 y = 0

integral of 9/(x-4)

\int \frac{9}{x - 4} d x

derivative of tan(4x^5)

\frac{d}{d x} (tan (4 x^{5}))

integral from 0 to 1 of 1/(x-2)

\int_{0}^{1} \frac{1}{x - 2} d x

limit as x approaches 2 of x^2sqrt(x)

x \to 2 lim (x^{2} x)

Frequently Asked Questions (FAQ)

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