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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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x = 1 \sum \infty \frac{( ( 2 x ) ^{x} )}{x ^{2 x}}

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\int \frac{2 x}{π} d x

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Frequently Asked Questions (FAQ)

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