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Popular >

derivative of arccos(arcsin(t))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

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x \to 0 lim (cos^{2} (x) \cdot x)

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n = 0 \sum \infty \frac{1}{n + 16}

(d^2y)/(dx^2)+a*y=0

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Frequently Asked Questions (FAQ)

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