Differentiate.

$($a$)y=\frac{6}{si{n}^{-1}(x)}$

$($b$)f(x)=xarctan(\sqrt[\phantom{2}]{x})$

Solution

$($a$)$

$\frac{dy}{dx}=\frac{d}{dx}[6(si{n}^{-1}(x){)}^{-1}]=()\frac{d}{dx}(si{n}^{-1}(x))$

$=$

$($b$)$

$f^{\text{'}}(x)=x()+arctan(\sqrt[\phantom{2}]{x})$

$=$