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

by RoRi

November 29, 2015

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 $|x| < 1$ .

One comment

January 19, 2021 at 6:07 am

Anonymous says:

The derivative of arccos x should be -1 / sqrt(1 – x^2), as opposed to the denominator of sqrt(1 – x^4)

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Stumbling Robot

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

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