Posted by Anonymous on Sunday, February 6, 2011 at 3:18pm.
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??
- calculus - bobpursley, Sunday, February 6, 2011 at 3:23pm
YOu are posting little work. Why don't you take the derivative of (3x)^.5 ?
it is a straight power series
y'= n u^(n-1) du/dx
If you cant do these, you need a tutor, it is as simple as it gets.
- calculus - Anonymous, Sunday, February 6, 2011 at 3:59pm
I'm going with B.
- calculus - Katie, Sunday, February 6, 2011 at 4:07pm
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)/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.
- calculus - Anonymous, Sunday, February 6, 2011 at 4:12pm
thanks katie i just needed to be reassured that my work was right . I'm not completly confident.
- calculus - Katie, Sunday, February 6, 2011 at 4:16pm
Your welcome. Don't worry you'll do good in your studies, keep it up
- calculus - Reiny, Sunday, February 6, 2011 at 4:17pm
The problem with multiple choice questions is that sometimes you might have the right answer, but in a different form
y = √(3x) = (3x)^(1/2)
dy/dx = (1/2)(3x)^(-1/2)(3)
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
- calculus - Anonymous, Sunday, February 6, 2011 at 4:22pm
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.
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