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Math Help - Time derivative

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    31

    Time derivative

    Hi,
    I have the following problem: I have a function to evaluate the obliquity of the ecliptic (astronomy) in the form:
    Code:
    f(t) = a + bt + ct^2 + dt^3
    Its derivative (rate) is:
    Code:
    derivative of f(t) = b + 2ct + 3dt^2
    Everything works out until here. But I've improved the formula; but now the t factor is equal to t/100;let's call it t', and with the new coefficients a', b', c' and d':
    Code:
    f_2(t') = a' + b't' + c't'^2 + d't'^3
    If I calculate f_2 for a given t the result is the same, but improved. But what about the derivative of f_2? It's:
    Code:
    derivative of f_2(t') = b' + 2c't' + 3d't'^2
    The rate, or derivative is referred to t' = t / 100; to referrer it to t, must I divide de derivative of f_2 by 100?
    Kind regards,
    Kepler
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  2. #2
    MHF Contributor

    Joined
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    Quote Originally Posted by kepler View Post
    Hi,
    I have the following problem: I have a function to evaluate the obliquity of the ecliptic (astronomy) in the form:
    Code:
    f(t) = a + bt + ct^2 + dt^3
    Its derivative (rate) is:
    Code:
    derivative of f(t) = b + 2ct + 3dt^2
    Everything works out until here. But I've improved the formula; but now the t factor is equal to t/100;let's call it t', and with the new coefficients a', b', c' and d':
    Code:
    f_2(t') = a' + b't' + c't'^2 + d't'^3
    If I calculate f_2 for a given t the result is the same, but improved. But what about the derivative of f_2? It's:
    Code:
    derivative of f_2(t') = b' + 2c't' + 3d't'^2
    The rate, or derivative is referred to t' = t / 100; to referrer it to t, must I divide de derivative of f_2 by 100?
    Kind regards,
    Kepler
    Yes, the derivative with respect to t' is [itex]b'+ 2c't+ 3d't'^2[/itex]. Now, by the chain rule, to get the derivative with respect to t, multiply by the derivative of t' with respect to t. Since t'= t/100, that is 1/100.
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