Math Is Fun Forum

caharris

Member

Registered: 2010-10-21

Posts: 4

Learning Calc

"If

and

be the lengths of a rod of iron at the temperatures t°C and 0°C respectively, then

. Find the change of length of the rod per degree Centigrade."

So I'm teaching myself calculus from the book Calculus Made Easy by Silvanus Thompson, and this is one of the exercises. I'm pretty sure it would be something like

.

I'd love a quick walk through if you can spare the time. I know how to find the differential when I'm working with (simple) equations, but word problems mess me up. Any help is appreciated.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Learning Calc

hi  caharris

yes, that's what you want.

The question intends that you treat

as a constant (it is the length at one temperature so is not a variable)

so you just need to differentiate

and multiply by

at the end.

Can you do the differentiation from this and complete the question?

Bob

Last edited by Bob (2011-01-03 08:00:34)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

caharris

Member

Registered: 2010-10-21

Posts: 4

Re: Learning Calc

So I'm basically working with

? Would it be

?

Last edited by caharris (2011-01-03 09:17:42)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Learning Calc

Hi caharris;

Welcome to the forum. You did not do that differentiation correctly.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

caharris

Member

Registered: 2010-10-21

Posts: 4

Re: Learning Calc

Hmmm... I was taught that if

, then

.

So

,

, then

?.

?

Sorry, I'm still new at this

Thank you guys for helping me out though

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Learning Calc

Hi;

You want to differentiate this.

Doing the 2 boxed derivatives one at a time.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

caharris

Member

Registered: 2010-10-21

Posts: 4

Re: Learning Calc

Ahh gotcha. Thank you so much!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Learning Calc

Hi caharris;

Your welcome, good luck in your studies. Come back if you need more.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.