How do you find the derivative of the function: $arccos (arcsin x)$ $arccos(arcsin x)$ ?

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Answer 1 · 2016-01-20T10:39:09

$\frac{d y}{d x} = - \frac{1}{\sqrt{1 - {(arcsin (x))}^{2}}} * \frac{1}{\sqrt{1 - x^{2}}}$ $dy/dx = -1/sqrt(1-(arcsin(x))^2)**1/sqrt(1-x^2)$

To find the derivative of $arccos (arcsin (x))$ $arccos(arcsin(x))$

The chain rule looks like a good choice here

Let $y = arccos (arcsin (x))$ $y=arccos(arcsin(x))$

Differentiating using $Chain Rule$ $color(magenta)"Chain Rule"$

$\frac{d y}{d x} = - \frac{1}{\sqrt{1 - {(arcsin (x))}^{2}}} * \frac{d}{d x} (arcsin (x))$ $dy/dx = -1/sqrt(1-(arcsin(x))^2)**d/dx(arcsin(x))$

$\frac{d y}{d x} = - \frac{1}{\sqrt{1 - {(arcsin (x))}^{2}}} * \frac{1}{\sqrt{1 - x^{2}}}$ $dy/dx = -1/sqrt(1-(arcsin(x))^2)**1/sqrt(1-x^2)$ Answer

How do you find the derivative of the function: arccos(arcsin x)arccos(arcsinx)arccos(arcsin x)?