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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (3 x ln (y) + y ln (z) - 4 x)

y = 3 sin (x^{3} - 5 x^{2} + 8 x + 0.5)

\int 2 x (x^{2} + 1)^{- 4} d x

\frac{7}{s ^{3} + 2 s ^{2} + 9 s + 18}

\int \frac{e ^{x}}{e ^{- 6 x}} d x

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