calculus
posted by Anonymous on .
6. What is the derivative of y = square root of 3x ?
a.dy/dx = square root of 3x/6x
b.dy/dx = square root of 3x/2x
c.dy/dx = 2 times the square root of 3x / 3x
d.dy/dx = square root of 3x/2
okay i know the answer might not be there but which one do you think is best. I don't know maybe B or c,d. i don't know??

YOu are posting little work. Why don't you take the derivative of (3x)^.5 ?
it is a straight power series
y= u^n
y'= n u^(n1) du/dx
If you cant do these, you need a tutor, it is as simple as it gets. 
I'm going with B.

For example, √x is the same as x^1/2, the derivative of √x is 1/2^ 1/2 equals to 1 / 2√x
sqrt(3x) = sqrt(3)sqrt(x)
and the derivative of this is
sqrt(3)*derivative(sqrt(x)) =
sqrt(3)/2sqrt(x), as d/dx (sqrt(x)) = 1/2sqrt(x).
now, multiply the top and bottom by sqrt(x), obtaining sqrt(3)sqrt(x)/2sqrt(x)sqrt(x) = sqrt(3x)/2x,
The correct answer is B. Try and work out the problem, it'll be easier for you. 
thanks katie i just needed to be reassured that my work was right . I'm not completly confident.

Your welcome. Don't worry you'll do good in your studies, keep it up

The problem with multiple choice questions is that sometimes you might have the right answer, but in a different form
here ....
y = √(3x) = (3x)^(1/2)
dy/dx = (1/2)(3x)^(1/2)(3)
= 3/(2√(3x)
now clearly that answer does not show up, even though it is correct.
However, if you multiply top and bottom by √(3x), rationalizing the denominator you do get
√(3x)/(2x) which is indeed b)
When you say, "I'm going with B", I sure hope that wasn't just a guess.
If you were just guessing then I agree 100% with
bobpursley's comments. 
no i didn't guess .i got = 3/(2ã(3x)
thats why i was confused . but then after going through it again I realized i can rationalize and katie post reassured me.