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}

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

\int_{8}^{14} \frac{y}{y ^{2} - 4 y - 5} d y

y^{^{'}} = e^{- 2 x}

t an g e n t f (x) = x^{2} + 1

7 y^{^{''}} + 5 y^{^{'}} + 7 y = 0

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)}