Thread: chain rule question

1. 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?

2. Originally Posted by johnbarkwith
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

3. but i want to find du/dT not du/dt...

4. Originally Posted by johnbarkwith
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)

5. by T(t) i meant T is a function of t.. why is it the case that du/dt should equal du/dT??

6. 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

7. 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 ??????????