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Math Help - chain rule question

  1. #1
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    chain rule question

    I am in the process of nondimensionalizing an ODE.

    I have the dimensionless variables u(s(t)) i.e. u which is a function of s which is a function of t, and T(t)....

    I am trying to find du/dT in terms of ds/dt, how do i go about doing this??

    I assume it just uses the chain rule, but havnt done anything like this for ages. could anyone help?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by johnbarkwith View Post
    I am in the process of nondimensionalizing an ODE.

    I have the dimensionless variables u(s(t)) i.e. u which is a function of s which is a function of t, and T(t)....

    I am trying to find du/dT in terms of ds/dt, how do i go about doing this??

    I assume it just uses the chain rule, but havnt done anything like this for ages. could anyone help?
    it is the chain rule.

    by the rule we have \frac {du}{dt} = u'(s(t)) \cdot s'(t)

    where s'(t) = \frac {ds}{dt} of course
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  3. #3
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    but i want to find du/dT not du/dt...
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by johnbarkwith View Post
    but i want to find du/dT not du/dt...
    it would be the same thing. well, should be, you were never very specific about T(t)
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  5. #5
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    by T(t) i meant T is a function of t.. why is it the case that du/dt should equal du/dT??
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  6. #6
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    I think he means

    they aer not "equal" but the same concept of \frac{d\bigg[f(g(x))\bigg]}{dx}=f'(g(x))\cdot{g'(x)} applies
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  7. #7
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    if im more specific, i have,

    T=aet

    u=s/c

    ds/dt = -aes + (d+as-fs)y +(as + g)h

    with a,e,d,f,g constants and s=s(t), y=y(t), h=h(t)


    i am trying to find du/dT ??????????
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