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

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

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

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

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derivative of

arcsin (x)

\frac{1}{2 x 1 - x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{2 x 1 - x}

\int_{5}^{10} a x - 10 b d x

f (x) = \frac{12}{x}, at x = - 2

\frac{d}{d z} (0)

x \to 0 lim (\frac{1}{x ^{\frac{1}{2}}})

\int (y e^{x} + sin (y)) d x

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