# Derivative of inverse trigonometric functions

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##### Examples

###### Lessons

- Review: what are "inverse trigonometric functions" ?

Find the measure of angle $\theta$ to the nearest degree:

- Use implicit differentiation to prove the formula:

$\frac{{d}}{{{d}x}}\left( {{{\sin }^{ - 1}}x} \right) = \frac{1}{{\sqrt {1 - {x^2}} }}$ - Calculate the derivative of $y=$ arccos $(x^2)$
- Calculate the derivative of $y=4$ arccot $(3x+1)$
- Calculate the derivative of $y= \frac{4 \arctan (e^x)}{x^2}$
- Calculate the derivative of $y=$ arcsec$\; x \;$arccsc$\; x$
- Prove that $\frac{d}{dx} [\tan^{-1}(4x^2)+ \cot^{-1}(4x^2)]=0$