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

The derivative of x/(sqrt(x^2-1)) is -1/((x^2-1)sqrt(x^2-1))

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

The first derivative of x/(sqrt(x^2-1)) is -1/((x^2-1)sqrt(x^2-1))

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

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

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

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

Simplify

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

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

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