What is the derivative of sqrt(arcsin(x)) ?

The derivative of sqrt(arcsin(x)) is 1/(2sqrt(arcsin(x))\sqrt{1-x^2)}

What is the first derivative of sqrt(arcsin(x)) ?

The first derivative of sqrt(arcsin(x)) is 1/(2sqrt(arcsin(x))\sqrt{1-x^2)}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to - 1 lim (1 - x^{2})

y = x^{2} - 2 x, at x = 0

\int \frac{ln ( x )}{x 1 + 7 ln ^{2} ( x )} d x

\frac{d y}{d x} = 2 y - 7 y^{3}

\frac{d}{d x} ((x)^{5 x})

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