Answer to Question #116789 in Calculus for Olivia

Question

Let u(t) and v(t) be vector-valued functions, and s,w be constant scalars. Which of the following statements is true?
Select one:
a. d/dt(su(t)+wv(t))=w(d/dtu(t))−s(d/dtv(t))


b. d/dt(sv(t)+wu(t))=w2(d/dtu(t))+s2(d/dtv(t))

c. d/dt(su(t)+wv(t))=w(d/dtu(t))+s(d/dtv(t))

d. d/dt(su(t)+wv(t))=s(d/dtu(t))+w(d/dtv(t))

Answer 1

The option 'd' is correct because

1. The constants are on their correct position i.e. s is with the derivative of u(t) and w is with the derivative of v(t).

2. The sign in the question between u(t) and v(t) is a plus sign and it stil jas to remain the same even after derivation.

3. There is no integer with any of the value of variables so the answer also need not to have any kind of integer added itself.

So i chose 'd' because it violates neither of basic rules.