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))

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

\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}}

\int \frac{1}{- 1 - y ^{2}} d y

\frac{d}{d x} (e^{x} - 3)

\frac{d y}{d t} + \frac{1}{t} y = \frac{6}{t}

\int \frac{1}{sin ^{2} ( x ) cos ( x )} d x

2 x, 4 x^{2}

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))