Calc homework - Chain Rule

audiobliss

I'm sitting here doing my Calc homework, and I need to understand the chain rule better than I do. I was going to wait and ask my instructor about it tomorrow, but it'd be really helpful if I knew it for this homework.

The chain rule: If F(x)=f(g(x)), then F'(x)=f'(g(x))g'(x).
For function that is the composite of three functions: If F(x)=f(g(h(x))), then F'(x)=f'(g(h(x)))g'(h(x))h'(x).

From that it appears that you start with the outside function, saying: prime of the outside function evaluated at the others, then prime of the next function in evaluated at the rest, and so on.

If F(x)=h(i(j(k(x)))), then it would follow given the above logic that F'(x)=h'(i(j(k(x))))(i'(j(k(x))))(j'(k(x)))(k'(x)).

Is that right?
Thanks a million!!!

audiobliss

:rolleyes:

Thanks for all the replies, guys!!

Ricardo

We have not replied because that one is too easy....... :rolleyes:

audiobliss

:eek:

gatemplin

Is that right?
Thanks a million!!!

Yeah that's exactly right. But that reminds me, I should be doing my own calc hwk.

audiobliss

Awesome!

I was looking at some notes from the instructor wrong, so I thought I had this all messed up, but I actually think I understand it now.

However, now I'm having problems applying the chain rule, I think. If f(x)=sqrt(25-x^2), then f'(x)=-x/(sqrt(25-x^2).

The problem is how the book got that. They just took the derrivative of f(x) by using the power rule and then took the derrivative of the inside function. I was seeing this problem as a composition of three functions, however they're obviously seeing it as a composition of two functions.

Question:
If I have F(x)=f(g(x)) and f'(x)=-1, what would I do with the g(x) in F'(x)=f'(g(x))? Would F'(x) just be -1? Because there's certainly no where in '-1' to plug in g(x). Or am I missing something?

gatemplin

audiobliss wrote:

Awesome!

I was looking at some notes from the instructor wrong, so I thought I had this all messed up, but I actually think I understand it now.

However, now I'm having problems applying the chain rule, I think. If f(x)=sqrt(25-x^2), then f'(x)=-x/(sqrt(25-x^2).

The problem is how the book got that. They just took the derrivative of f(x) by using the power rule and then took the derrivative of the inside function. I was seeing this problem as a composition of three functions, however they're obviously seeing it as a composition of two functions.

The simplest way to do that IMO is,

f(x) = sqrt(25-x^2)

f(x) = (25-x^2)^1/2

f'(x) = ((1/2)(25-x^2)^-1/2)(-2x) = -x/((25-x^2)^-1/2)

Question:
If I have F(x)=f(g(x)) and f'(x)=-1, what would I do with the g(x) in F'(x)=f'(g(x))? Would F'(x) just be -1? Because there's certainly no where in '-1' to plug in g(x). Or am I missing something?

Right. In that case F'(x) is -1 but that is a messed up question. The function f'(x) evaluated anywhere is always -1.

audiobliss

That's how the book did that problem. So I guess it is a good way to do it, huh? lol


Why is that a messed up question?

Thanks for your help! I think I understand it now.

Thanks!!
Michael

Markymark

darn... I miss that stuff. It was easy

lanion

Yeah I have a question on my quantum homework...

Schris22

theres too many parenthesis...

()()(()((((())))))

I had calc 2 years ago and all i remember is use a ti 89 and solve for x

nadams

audiobliss- do you actually ever do your own homework?

audiobliss

Schris22 wrote:

I had calc 2 years ago and all i remember is use a ti 89 and solve for x

That Ti-89 is why that's all you remember, lol.

Nadams - Yes, actually. Well, um....errrrr, uhhh, ummmm, ...... Actually, you'll notice I haven't asked you to solve any problems. I'm just asking about concepts.


I talked to the instructor this morning about it and it really cleared it up. I have no idea why I was being so dense about it. It really is a simple concept. Now I have to review implicit differentiation, too, because I didn't fully understand that one, either.

gatemplin

audiobliss wrote:

That Ti-89 is why that's all you remember, lol.

Now I have to review implicit differentiation, too, because I didn't fully understand that one, either.

Yeah my math professors dont allow us to use calculators for that reason, they say they are "evil".

Implicit diff isn't too bad, all this stuff just takes lots and lots of practice. You'll get it I'm sure. Do as many of the hardest problems you can too. You'll make faster progress wrestling the bigger problems.

As John von Neumann said: "In mathematics you don't understand things. You just get used to them"

ohskigod

TI-89, thats a blast from the past. that caculator was the **** when I was in school

lanion

I was in a Mathematica program for my h.s. calc class... but even Mathematica is kind of worthless for a lot of college math / physics.

Serendipity

audiobliss wrote: »

That Ti-89 is why that's all you remember, lol.

Nadams - Yes, actually. Well, um....errrrr, uhhh, ummmm, ...... Actually, you'll notice I haven't asked you to solve any problems. I'm just asking about concepts.


I talked to the instructor this morning about it and it really cleared it up. I have no idea why I was being so dense about it. It really is a simple concept. Now I have to review implicit differentiation, too, because I didn't fully understand that one, either.

To make you feel better, I still haven't figured out how to use all the functions in the TI-89

jakelm

I'm using a TI 5035II and dont know all the functions. I do know that the red ink is negative...:p

"Today in class we will learn and study the new claculator we will be using, then eventually get to the class subject."

rskarvan

I sort-of, kind-of remember the chain rule. Haven't yet used it once in 20 some years working as an engineer.

Serendipity

rskarvan wrote: »

I sort-of, kind-of remember the chain rule. Haven't yet used it once in 20 some years working as an engineer.

Brings a new meaning to the phrase "When will I ever need this in my life?" to us engineers.

I'm studying to be one too

rskarvan

The primary purpose of teaching math is to really learn logical thinking and to practice problem solving skills. That is the real value of an engineering education.

Serendipity

I guess you're right. Engineering is fun though

audiobliss

Dangit. Back when I originally started this subject, I really really really enjoyed math and was seriously thinking about becoming a math professor at a college or an engineer.

Then came calc 2 and calc 3, and I continued to practice my skills of coasting through classes getting good grades learning zilch. So as I was on my way to a 'B' in cal 3 I realized that I really don't understand math enough to start teaching it. So then I started focusing on computer science or the medical field for a career.

But then today at work (I work as a math tutor at school) it again hit me how much I love math. So now I'm actually contemplating the idea of teaching math again.



Man, this life is so confusing!

petrym

Chain Rule, okay... chain gun:

<object width="425" height="355"><param name="movie" value="http://www.youtube.com/v/Ms-3tA-TT8U&rel=1"></param><param name="wmode" value="transparent"></param><embed src="http://www.youtube.com/v/Ms-3tA-TT8U&rel=1&quot; type="application/x-shockwave-flash" wmode="transparent" width="425" height="355"></embed></object>

Sorry for the derail, but I fired miniguns and .50's off of MH-53J PAVE LOW III's in Korea. That's the Chain RULE. <hides back in corner>

[Deleted User]

audiobliss, wait til you get into engineering math or linear algebra.. You wanna talk about time consuming! Derivatives and anti, I would love to help you but its been ages, well like 10 or so years since I messed with that stuff. Tip: (nothing about race okay guys) find the asians that you always see at school day and night, those freaks are mind boggling! And if that does not work out, HP, is like a genius in your palm, its just me though, I am anti TI aside from DLP!

Serendipity

audiobliss wrote: »

Dangit. Back when I originally started this subject, I really really really enjoyed math and was seriously thinking about becoming a math professor at a college or an engineer.

Then came calc 2 and calc 3, and I continued to practice my skills of coasting through classes getting good grades learning zilch. So as I was on my way to a 'B' in cal 3 I realized that I really don't understand math enough to start teaching it. So then I started focusing on computer science or the medical field for a career.

But then today at work (I work as a math tutor at school) it again hit me how much I love math. So now I'm actually contemplating the idea of teaching math again.



Man, this life is so confusing!

So have you decided yet, computer science or med school?

audiobliss

appadv wrote: »

So have you decided yet, computer science or med school?

...or teaching, or engineering, or mechanic, or preacher, or....

...ugh, you catch my drift...

Serendipity

audiobliss wrote: »

...or teaching, or engineering, or mechanic, or preacher, or....

...ugh, you catch my drift...

Whatever you do, I'm sure you'll be good at it.

Now get back to studying!