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)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\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}}

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)}