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Popular >

derivative of (arcsin(x))^3

Solution

derivative of

(arcsin (x))^{3}

Solution

\frac{3 arcsin ^{2} ( x )}{1 - x ^{2}}

Solution steps

\frac{d}{d x} ((arcsin (x))^{3})

Apply the chain rule:

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

= 3 (arcsin (x))^{2} \frac{d}{d x} (arcsin (x))

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

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

Simplify

3 arcsin^{2} (x) \frac{1}{1 - x ^{2}} : \frac{3 arcsin ^{2} ( x )}{1 - x ^{2}}

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

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Frequently Asked Questions (FAQ)

What is the derivative of (arcsin(x))^3 ?
The derivative of (arcsin(x))^3 is (3arcsin^2(x))/(sqrt(1-x^2))
What is the first derivative of (arcsin(x))^3 ?
The first derivative of (arcsin(x))^3 is (3arcsin^2(x))/(sqrt(1-x^2))