calculus

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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 -

    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^(n-1) du/dx

    If you cant do these, you need a tutor, it is as simple as it gets.

  • calculus -

    I'm going with B.

  • calculus -

    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.

  • calculus -

    thanks katie i just needed to be reassured that my work was right . I'm not completly confident.

  • calculus -

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

  • calculus -

    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.

  • calculus -

    no i didn't guess .i got = 3/(2ã(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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