$3$ senau sat Ans :

$|x|\sqrt[\phantom{2}]{x^2-1}$

$dx$

$|x|\sqrt[\phantom{2}]{x^2-1}$

Example $2$ Find the following derivatives.

$($a$)\frac{d}{dx}[co{s}^{-1}(x^2-1)]$

$($b$)\frac{d}{dx}[sin(co{s}^{-1}x)]$

Example $3$ Evaluate $f^{\text{'}}(1),$ where $f(x)=xta{n}^{-1}(x^2).$