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Popular >

derivative of x/(x^2-1)

Solution

derivative of

\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}}

Graph

Popular Examples

integral of 6e^{3x}-8/(e^{2x)}

\int 6 e^{3 x} - \frac{8}{e ^{2 x}} d x

y^{''}-4y^'+4y=(x+1)e^{2x}

y^{^{''}} - 4 y^{^{'}} + 4 y = (x + 1) e^{2 x}

tangent of f(x)= 1/(sqrt(8x)),\at (x=9)tangent of

f (x) = \frac{1}{8 x}, at (x = 9)

sum from n=0 to infinity of (2^n)/((2n)!)x^{2n}

n = 0 \sum \infty \frac{2 ^{n}}{( 2 n ) !} x^{2 n}

limit as x approaches 7-of (x-7)/(|x-7|)

x \to 7 - lim (\frac{x - 7}{∣ x - 7 ∣})

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)