What is the derivative of (arcsin(2x)^2) ?

The derivative of (arcsin(2x)^2) is (4arcsin(2x))/(sqrt(1-4x^2))

What is the first derivative of (arcsin(2x)^2) ?

The first derivative of (arcsin(2x)^2) is (4arcsin(2x))/(sqrt(1-4x^2))

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

\frac{4 arcsin ( 2 x )}{1 - 4 x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (arcsin (2 x)) = \frac{2}{1 - 4 x ^{2}}

= 2 arcsin (2 x) \frac{2}{1 - 4 x ^{2}}

Simplify

2 arcsin (2 x) \frac{2}{1 - 4 x ^{2}} : \frac{4 arcsin ( 2 x )}{1 - 4 x ^{2}}

= \frac{4 arcsin ( 2 x )}{1 - 4 x ^{2}}

What is the derivative of (arcsin(2x)^2) ?
The derivative of (arcsin(2x)^2) is (4arcsin(2x))/(sqrt(1-4x^2))
What is the first derivative of (arcsin(2x)^2) ?
The first derivative of (arcsin(2x)^2) is (4arcsin(2x))/(sqrt(1-4x^2))