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Math Help - Derivative parametricly given function.

  1. #1
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    Derivative parametricly given function.

    Can someone please give me formulas and explanations to these

    y' and y'' or just y^(n) from xx / xy / yy (i hope that "from" is the right way how to say it, maybe "by")

    when i have { x=ch[t], y=(sh^2[t])^1/3 }

    Or maybe explayning which one from above is equal to this:

    y'' from xt * t' from x

    and if y' from x = y' from t / x' from t, is y' from y the same turned around? or that would be x' from y?

    basicly i need all kind of formulas for my notes x:
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  2. #2
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    This entire post is extremely difficult to understand. We understand that English might not be your first language, but the policy of this forum is that you write your posts in comprehensible English. Just about everything in the OP needs rephrasing.
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  3. #3
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    Quote Originally Posted by Ackbeet View Post
    This entire post is extremely difficult to understand
    OK, so with y'' from xx i ment

    an replacing "y'' from xx" to " y''[xx] " folows

    y', y'' or just y^(n) from xx / xy / yy

    when i have {
    x=ch[t]
    y=(sh^2[t])^1/3
    }

    Or maybe explayning which one from above is equal to this: y''[xt] * t'[x]

    and if y'[x] = y'[t] / x'[t], is y'[y] the same turned around? or that would be x'[y]?

    can you now understand what i ment with it?
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  4. #4
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    Vaguely better. It is still not very good English. It looks like you are trying to find some derivative of a parametrically defined function. Is that correct? If so, let me ask these questions:

    1. Exactly what derivative are you trying to find? Are you trying to find \dfrac{d^{2}y}{dx^{2}}?
    2. What is ch(t)? Is that the hyperbolic cosine function? If so, the usual notation is cosh(t).
    3. What is sh(t)? Is that the hyperbolic sine function? If so, the usual notation is sinh(t).
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  5. #5
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    Yes, i need formulas to derivative a parametrically defined function. (as in title sayd)
    I'm sorry if my english isn't as good as you would like it to be.

    I know that f''(x)=(f'(x))'.



    I'm not sure about the 2nd and 3rd questions, but from formulas which i have been given: sh'(x)=ch(x) and ch'(x)=sh'(x), but that isn't important in my question.

    I was showing {x=... , y=...} just in case. I'm not asking to solve my example, i'm asking formulas for y^(n)[xx or xy or yy] where y^(n) is the same as d^n*y/dx^n, if you know only that way of writing it.

    Do you still dont understand what i'm asking?

    EDIT: I found some formulas. Can you (forum) approve that they're right?



    EDIT#2: Lets do it like this: soleve me my example and i will figure out what i need from it myself.

    {
    x=arcsin(t)
    y=ln(1-t^2)
    }

    Y''[xx] - ?

    Y''[xy] - ?
    Last edited by kakaini; October 15th 2010 at 11:08 AM.
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  6. #6
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  7. #7
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    Quote Originally Posted by zzzoak View Post
    That would be y''[xx].

    Y''[xy]. ?
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  8. #8
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    You have function
    y(x)
    or
    y(x(t)) = y(t) and x(t).
    There is no derivative
    <br />
y_{xy}.<br />

    If you have function
    z(x,y)
    or z(x(t),y(t))=z(t) and x(t), y(t)
    then you may have
    <br />
z_{xx}, \; z_{xy}, \; z_{yy}. <br />
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