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Popular >

derivative of arcsin(9/(x^2))

Solution

\frac{d}{d x} (arcsin (\frac{9}{x ^{2}}))

Solution

- \frac{18}{x x ^{4} - 81}

Solution steps

\frac{d}{d x} (arcsin (\frac{9}{x ^{2}}))

Apply the chain rule:

\frac{1}{1 - ( \frac{9}{x ^{2}} ) ^{2}} \frac{d}{d x} (\frac{9}{x ^{2}})

= \frac{1}{1 - ( \frac{9}{x ^{2}} ) ^{2}} \frac{d}{d x} (\frac{9}{x ^{2}})

\frac{d}{d x} (\frac{9}{x ^{2}}) = - \frac{18}{x ^{3}}

= \frac{1}{1 - ( \frac{9}{x ^{2}} ) ^{2}} (- \frac{18}{x ^{3}})

Simplify

\frac{1}{1 - ( \frac{9}{x ^{2}} ) ^{2}} (- \frac{18}{x ^{3}}) : - \frac{18}{x x ^{4} - 81}

= - \frac{18}{x x ^{4} - 81}

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Frequently Asked Questions (FAQ)

What is the derivative of arcsin(9/(x^2)) ?
The derivative of arcsin(9/(x^2)) is -(18)/(xsqrt(x^4-81))
What is the first derivative of arcsin(9/(x^2)) ?
The first derivative of arcsin(9/(x^2)) is -(18)/(xsqrt(x^4-81))