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?

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

What  $\left[ \frac{x^2+4}{y^2+4} \frac{dy}{dx} \left( x^2+4 \frac{d^2y}{dx^2} - 16y \right) \right] $  equal to?