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?

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

Consider the following statements:

I. The function is differentiable at x = 3

II. The function is differentiable at x = 4

Which of the statements given above is/are correct?