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# chain rule watch

1. i am stuck on these questions of showing things are true via the chain rule

show by the chain rule that,

dx/dt = 1/t(dx/ds)

d^2x/dt^2 = 1/t^2(d^2x/ds^2) - 1/t^2(dx/ds)

you are told that t = e^s (or s = lnt)

thanks
2. Um, you might want to give us whatever information you have about s and t...
3. sorry I edited my original post would appreciate some help
4. Okay. Well, the chain rule says that dx/dt = (dx/ds)(ds/dt), and you can work out ds/dt from what you know about s and t. After that, let y = dx/dt; then d^2x/dt^2 = dy/dt.
5. bumping this thread for a question:

for the first one, I got dx/dt = dx/ds * ds/dt, and ds/dt is differentiating lnt, so it's 1/t. so i did the first one.

however, the second one, i differentiated the first one using the product rule. I got d^2x/dt^2 = 1/t(d^2x/ds^2) - 1/t^2(dx/ds)

I am missing out a t^2 on the bottom of the first fraction. any ideas where i have gone wrong? thanks

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Updated: February 5, 2010
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