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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 3 lim (3 x + 9)

\frac{d}{d x} (2 x e^{y})

\int - 4 d x

\frac{\partial}{\partial y} (3 x - 4 y)

\int e^{x} cos (n x) d x

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