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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 3 y^{5} y^{3} + 1 d y

x \to - 1 lim (x + 2 x^{4})

\frac{d}{d x} (a x e^{- x})

\frac{\partial}{\partial x} (ln (a x + b y))

n = 1 \sum \infty (1)^{n}

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