For the following three (03) items:
Let $y=f(x)=\frac{x\sin ^{-1}x}{\sqrt{1-x^{2}}}+\ln \sqrt{1-x^{2}}.$

If x = sin $\theta$ then what is $\frac{dy}{dx}$ equal to?
 

For the following two (02) items:
Consider the function $f(x)=1-\sqrt[3]{(x-1)^{2}}$

What is the domain of the function?

For the following two (02) items:
Consider the function $f(x)=1-\sqrt[3]{(x-1)^{2}}$

The function has

For the following two (02) items:
Consider the function
$f(x)=\begin{cases}4(5^{x}),&x<0\\ 8k+x,&x\ge 0\end{cases}$

If the function is continuous, then what is the value of k?