derivative question...?

Question

a few actually

1. sqrt(x) is this just x?
2.(3/sqrt(x)) what is that one? zero??
3. 6sqrt(x) would that be just 6x??

Answer 1

1: f(x) = sqrt(x) = x^(1/2)
f'(x) = (1/2) x^(-1/2) = 1 / (2 sqrt(x))

2: f(x) = 3/sqrt(x) = 3 / x^(1/2) = 3x^(-1/2)
f'(x) = 3(-1/2)x^(-3/2)
= -(3/2)/ (x^3/2)
= -3/(2x sqrt(x))

3: f(x) = 6 sqrt(x) = 6 x ^(1/2)
f'(x) = 6(1/2)x^(-1/2)
= 3 / (x^(1/2))
= 3 / sqrt(x)

Answer 2

Just remember that taking the square root of something is the same thing as raising it to the 1/2 power (and taking any other root is raising to 1 over the root, i.e. sqrt(x) = x^(1/2), cuberoot(x) = x^(1/3), etc.)

Answer 3

You haven't benn paying -any- attention at all in class, have you? (To say nothing of not having read your textbook)
You don't have -any- of them even close to correct. The first one is
1/(2√x) and now you best get your butt in gear and figure out how the rest of them work because theres a test with a 'F' on it in your near future if you don't.

Doug