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Popular >

derivative of arcsin(sqrt(x^2-1))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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\frac{\partial}{\partial y} (ln (\frac{y}{x}))

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Frequently Asked Questions (FAQ)

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