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Find the derivative of (arccos (x2))-2

Find the derivative of the function

    \[ f(x) = \frac{1}{(\arccos(x^2))^2}. \]


Here we use the power rule, the chain rule, and the formula for the derivative of the arccosine,

    \begin{align*}  f'(x) &= (-2)(\arccos(x^2))^{-3} (2x) \left( \frac{-1}{\sqrt{1-x^4}} \right) \\  &= \frac{4x}{\sqrt{1-x^4} (\arccos(x^2))^3}. \end{align*}

The formula is valid for |x| < 1.

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