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
$f(x)=\begin{cases}4(5^{x}),&x<0\\ 8k+x,&x\ge 0\end{cases}$

What is f'(-1) equal to?

For the following two (02) items:
Let the function f(x) = |x - 3| + |x - 4| be defined on the interval [0, 5].

What is $\frac{dy}{dx}$ at x = 3.5 equal to?

Let  $x = \sec \theta - \cos \theta \text{ and } y = \sec^4 \theta - \cos^4 \theta \\ $ 

What is $(\frac{dy}{dx})^2$ equal to?