Math Is Fun Forum

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Stuck on a chain rule prob

Hi All

I have been doing o.k with this stuff so far, but have hit a block with one of them.

here it is.

if I do

and

i can't get the required

from

i suppose what I am asking is how do I split this up into two functions.

Cheers

Dave

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Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Stuck on a chain rule prob

Hi Dave;

Why do you need to use the chain rule?

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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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Stuck on a chain rule prob

Hi all,

Dave, The chain rule is

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Stuck on a chain rule prob

Hi;

I suggest memorizing this one. For the next 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.

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Stuck on a chain rule prob

Hi huys

I'm just following this book I have and the questions are supposed to get you
used to using and understanding the idea. Up until this one they pretty much
the same. Some log, some trig some simple composite functions.

in the book it says the chain rule is

this works fine for

The problem is I don't know how to handle to 6x^2 term, in terms a composite function.

if i make

and

i then make

it is on

where I get stuck.

---

Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Stuck on a chain rule prob

Hi Dave;

Can you finish now?

---

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Stuck on a chain rule prob

Hi dave,

From the equation:

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Stuck on a chain rule prob

hi Dave,

I've been away so I've only just read this thread.

This is what I think is causing you difficulty.

Some functions can be differentiated using the basic rule

eg.

Then some functions will be simple functions added or subtracted.

For these you may differentiate each bit and then add or subtract the results.

eg.

Then you have the ones where the chain rule applies. 

y is a function of say u, where u is a function of x.  That's when you have to use

eg.

(There's also the product and quotient rules but I'll skip over these for now, in case you haven't done these yet.)

Once you've got the basics of each process the exercises start to get harder by muddling up bits of one method with bits of another.

In

you have a chain rule and a sum, with the second bit just a simple differentiation.

You're meant to spot that the first bit needs the chain rule
and the second bit can be just differentiated using the 'multiply by the power and drop the power by one' rule.

So you only need the chain rule for the first half of the function.  I've done that above as an example.
And I've also done the second bit in an example above.  So just add the two results together.

I've added a little diagram to show when the chain rule is needed.  When you meet the product and quotient rules I've got diagrams for them too.  That should help you to decide which rule to apply when.

Bob

Last edited by Bob (2011-08-07 06:59:47)

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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

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Stuck on a chain rule prob

Hi All

I think I get it now. So in this one the chain rule is only supposed to be used on the
first e term and then the

term is done separately on its own at
the end.

Something like this.

This book never even mentioned anything of the sort. Though I suppose it is meant
for tutored lessons.

---

Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Stuck on a chain rule prob

Hi;

That is what I meant in my first post. The 6x^2 is a power rule and even the exponential term can be done by a rule. But if you you are forced to use the chain rule you would only use it on the e^(3x).

Differentiation is a linear operator meaning that you apply it term by term.

---

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.

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Stuck on a chain rule prob

Hi Bobby

Thanks for that.

Yes I understand now. Just worked the rest of the remaining problems on the exercise
and got them all.

More reading needed though.

---

Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Stuck on a chain rule prob

Hi Dave;

Glad to hear you got them right, Post any you get problems on.

How are you doing, I have not heard from you in a while?

---

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.

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Stuck on a chain rule prob

Yes I am good. Supposed to be starting work this week, the place
called last week to say they were moving all their kit over to a new
office and then getting me in after that. All excited

Other than that just been going over things I have forgotten and trying
to get MATLAB to do fractals. This has of course meant brushing up on
complex numbers and infinite series.

I sort of understand how it works, but not enough to get it to work inside
MATLAB.

Maybe I should start a new post on that?

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Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Stuck on a chain rule prob

Hi DaveRobinsonUK;

Good luck with the new job! You will do fine.

Matlab, unfortunately that is one I do not use.

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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.