x Turn on thread page Beta
 You are Here: Home >< Maths

# maths question watch

1. i created a thread on the chain rule, bumped it today. created a new thread because i figured threads with 0 replies are ones which people looks at even if the OP hasnt had their question answered.

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

show by the chain rule that,

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

2. 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)

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 correctly.

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 (the bold bit is wrong). i cant think of how to get a t^2 there. any ideas where i have gone wrong? thanks
2. When you differentiated the second time, what did you differentiate with respect to? I think you've sort of done duv/dt = vdu/ds + udv/dt.
3. (Original post by IrrationalNumber)
When you differentiated the second time, what did you differentiate with respect to? I think you've sort of done duv/dt = vdu/ds + udv/dt.
i just followed the product rule, ignoring what i was differentiating with respect to. how do you do it, i have been stuck for ages on this thing
4. 2. d^2x/dt^2 = 1/t^2(d^2x/ds^2) - 1/t^2(dx/ds)
You just forgot to get d/dt in terms of ds

Using product rule:

Now looking at the relationship for t and s we see that

so therefore

This implies that

Substitute this in the earlier expression to get

Which gives the desired result.
5. (Original post by wrooru)
i just followed the product rule, ignoring what i was differentiating with respect to. how do you do it, i have been stuck for ages on this thing
Well that's why it went wrong, you have to consider what you're differentiating with respect to.

duv/dx = vdu/dx + udv/dx. You can't infer from that that
duv/dt=vdu/ds + udv/dt... It should be duv/dt=vdu/dt+udv/dt. You can then use the chain rule on du/dt to get du/ds * ds/dt...

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 5, 2010
Today on TSR

### Did he block me?

What should I do?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE