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 $u=\int e^{x}cos~x~dx $ and $v=\int e^{x}sin~x~dx.$

What is u + v equal to?

For the following two (02) items:
Let $u=\int e^{x}cos~x~dx $ and $v=\int e^{x}sin~x~dx.$

Consider the following:
I. $\frac{du}{dx}=-v $
II. $\frac{dv}{dx}=-u$
Which of the above is/are correct?

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?