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Math Help - Differenciation

  1. #1
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    Differenciation

    am trying to differentiate these equations
    y = tan^2(x)^3 + cos 2x and

    y=(e^x)^2/ln(2x)
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  2. #2
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    Quote Originally Posted by sigma1 View Post
    am trying to differentiate these equations
    y = tan^2(x)^3 + cos 2x and

    y=(e^x)^2/ln(2x)
    1) Chain rule.

    2) Quotient rule.
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  3. #3
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    i know that but am having a bit of problem separating the variable that is making something "U" . i would like to see how it is done if that is not too much of a trouble. am trying to catch up quickly on calculus.
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  4. #4
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    U substitution is a topic for integration, not differentiation. If you can show us your work, we will be more than happy to help point you in the right direction.

    You may also want to check out this link, which covers product, quotient and chain rules for differentiation: Product Rule, Quotient Rule, and Chain Rule Tutorial
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  5. #5
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    Just in case a picture helps...



    ... where


    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (which is the inner function of the composite and hence subject to the chain rule).

    Spoiler:


    ... and the inner differentiation zoomed in...


    ________________________________________
    Don't integrate - balloontegrate!

    Balloon Calculus: Standard Integrals, Derivatives and Methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
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  6. #6
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by sigma1 View Post
    am trying to differentiate these equations
    y = tan^2(x)^3 + cos 2x and

    y=(e^x)^2/ln(2x)
    1. the derivative of  tan^{2}(x)^3  = 2tan(x^3)sec^2(x^3) 3x^2

    Likewise find out the derivaitve of cos2x and add them up

    2. try the quotient rule, show how much effort you put on this problem. Post if you have any errors and they will be fixed.
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  7. #7
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by sigma1 View Post
    am trying to differentiate these equations
    y = tan^2(x)^3 + cos 2x and

    y=(e^x)^2/ln(2x)[/tex]
    I'll help you a bit with the first one to get you started

     y = tan^2(x)^3 + cos 2x

    Now let  p = tan^2(x)^3, q = cos2x

    We want Y` so

     y` = p` + q`

    This makes it easy, all we need to do is differentiate P and Q seperately and then add them up!

    Well Q` is fairly easy

     q` = -2sin2x

    I leave tan^2(x)^3 to you. But I would like to let you know that

     Tan^2x = Sin^2x/Cos^2x

    This might make it easiar to apply quotient rule?
    Last edited by AllanCuz; April 9th 2010 at 05:22 PM.
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  8. #8
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    Quote Originally Posted by AllanCuz View Post
    I'll help you a bit with the first one to get you started

     y = tan^2(x)^3 + cos 2x

    Now let  p = tan^2(x)^3, q = cos2x

    We want Y` so

     y` = p` + q`

    This makes it easy, all we need to do is differentiate P and Q seperately and then add them up!

    Well Q` is fairly easy

     q` = {\color{red}-} 2sin2x Mr F edit: Correction. The red negative is required.

    I leave tan^2(x)^3 to you. But I would like to let you know that

     Tan^2x = Sin^2x/Cos^2x

    This might make it easiar to apply quotient rule?
    To differentiate p = \tan^2 (x^3) it might be easier to use the product rule and differentiate \tan (x^3) using the chain rule.
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  9. #9
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by mr fantastic View Post
    To differentiate p = \tan^2 (x^3) it might be easier to use the product rule and differentiate \tan (x^3) using the chain rule.
    I was too lazy to actually compute it so maybe! Thanks for the negative by the way, lol to much time spent studying on my own exams that I forget to add the easy stuff
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  10. #10
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    thanks alot guys i did it and i seem to get the answer by letting

    then

    to get du/dx of i had to apply the chain rule again

    now i dIfrenciated and i got is that correct
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  11. #11
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by sigma1 View Post
    thanks alot guys i did it and i seem to get the answer by letting

    then

    to get du/dx of i had to apply the chain rule again

    now i dIfrenciated and i got is that correct
    Yes it is. And the differentiation of tan^2(x)^3 is in one pf the above posts
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