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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{e ^{- 5 s}}{s ^{2} - 4 s + 13}

y^{^{''}} = 2 + x

(1 + x) \frac{d y}{d x} = 4 y

x (x - 2) \frac{d y}{d x} + 2 y = 0

\frac{d}{d x} (4 x^{3} + \frac{1}{x ^{2}})

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