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Math Help - Can someone help me find the derivative?

  1. #1
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    Can someone help me find the derivative?

    i cant seem to find the derivative of the following functions, and ive been trying to solve them for close to 4 hours. ive used quotient rule, product rule, chain rule but i still dont get the answers. here they are:

    2x^3 - 1 all over x^2

    root x(x^3 - x)

    root(x-1)(x +1)

    ((root x) + 2)^-2/3

    please help!!
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  2. #2
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    1. 2+2/x^3
    2. root(x^2 - 1)+x^2/root(x^2 - 1)
    3. x/root(x^2-1)
    4. -(root(x)+2)^(-5/3)/(3*root(x))
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  3. #3
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    how did you get these answers tho? mainly number 1, because i keep getting 2x^4 + 2x all over x^4
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  4. #4
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    Ok. In the first problem. Separate each term. So you'll get two terms. 2x and -1/x^2. Then take the derivatives for both seperately. you'll get the answer.
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  5. #5
    Super Member Matt Westwood's Avatar
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    Take a look at 2x^4 + 2x all over x^4, and compare it with 2 + 2/x^3.

    For example, multiply top and bottom of 2/x^3 by x, then add it to 2 using the standard techniques of addition of fractions.

    What do you notice ...?
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  6. #6
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    Also, I think I may have taken the root over everything in the second and third problem. If that's what the question is then the answers above are right. Also, the second and thirs question I just used the chain rule.
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  7. #7
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    Ooops. Did not see that. Anyway, that is the right answer. Use it this way or that way.
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  8. #8
    Super Member Matt Westwood's Avatar
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    Finding derivatives is completely mechanical.

    If you don't get the answers you think you ought to get (e.g. by comparing them with the answers) then:

    a) You've done something incorrect when you used the mechanical procedure, or:
    b) You *have* got the same result as the answer book, but you haven't completed the algebraic manipulation to prove they are in fact identical.

    You've told us what you got for Q1, which shows it's an example of (b). You have not told us what you got for 2, 3 and 4. Before we go any further, that would be a good idea, because then we will know what you have done. Then we will be able to help properly.

    Except I'm going off line now because I have a long day tomorrow and it's nearly 11:30 where I am.
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  9. #9
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    Quote Originally Posted by DamienM View Post
    i cant seem to find the derivative of the following functions, and ive been trying to solve them for close to 4 hours. ive used quotient rule, product rule, chain rule but i still dont get the answers. here they are:

    2x^3 - 1 all over x^2

    root x(x^3 - x)

    root(x-1)(x +1)

    ((root x) + 2)^-2/3

    please help!!
    You can do them all at WolframAlpha: eg. differentiate Sqrt[x(x^3 - x)] - Wolfram|Alpha

    Click on Show steps.


    in future, please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. See rule #8: http://www.mathhelpforum.com/math-he...ng-151418.html.

    Thread closed.
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