Derivative of inverse trigonometric functions

Lessons

1. Review: what are "inverse trigonometric functions" ?
   
   Find the measure of angle $\theta$ to the nearest degree:
   
   
2. Use implicit differentiation to prove the formula:
   $\frac{{d}}{{{d}x}}\left( {{{\sin }^{ - 1}}x} \right) = \frac{1}{{\sqrt {1 - {x^2}} }}$
3. Calculate the derivative of $y=$ arccos $(x^2)$
4. Calculate the derivative of $y=4$ arccot $(3x+1)$
5. Calculate the derivative of $y= \frac{4 \arctan (e^x)}{x^2}$
6. Calculate the derivative of $y=$ arcsec$\; x \;$arccsc$\; x$
7. Prove that $\frac{d}{dx} [\tan^{-1}(4x^2)+ \cot^{-1}(4x^2)]=0$