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Popular Calculus >

derivative of arcsin(a/x)

Solution

\frac{d}{d x} (arcsin (\frac{a}{x}))

Solution

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

Solution steps

\frac{d}{d x} (arcsin (\frac{a}{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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