Calculus problems

[LuDaCriS66]

This is just great... first year of calculus and I know absoleutly nothing! I'm lost beyond belief in this class.. I've been terrible at math since I entered high school... and I mean horrible! I've never had a grade over 70% in any math class..

I know there are online tutorial sites such as www.ihatecalculus.com but they're still confusing to me. I have a test coming up on derivatives and the such and I'm completely lost.

What the heck is the difference between all those rules?? The product rule, quotient rule, power rule, the sum and difference rule, and the chain rule. Also there's implicit differentiation.

How am I supposed to know when to use which rule?? You can see how lost I am.

And what's that dy/dx thing? Ah geez.. I'm so screwed.

 

[JohnnyReb]

And what's that dy/dx thing? Ah geez.. I'm so screwed

You need a tutor. Have you been studying or slacking? Have you gone to your prof?

John

 

[notfred]

Use the product rule when you're multiplying functions, ie: sinx(x^2+2x+4)

Use the quotient rule when you're dividing functions, ie: (x^2+2x+4)/(sinx)

use the power rule when you have exponents: f(x) = x^n, f'(x)=nx^(n-1)

use the chain rule when you've got functions attached to each other in wierd ways: sin^3(X^2+4)

sum and difference are jsut addition and subtraction.


All this stuff is pretty basic.

 

[LuDaCriS66]

<< And what's that dy/dx thing? Ah geez.. I'm so screwed

You need a tutor. Have you been studying or slacking? Have you gone to your prof?

John >>



I definately need a tutor... I've been trying to study but I can't even understand the first chapter let alone study the second.. and this is for high school.. which is even worse cuz this class pretty much determines whether I get into post secondary schools or not.. I've talked to my teacher but he isn't much help.. I clearly can't understand his teaching style.. he just puts some questions up on the board.. and works them out but doesn't explain it fully.. it's like he expects us to know understand every single step. I can't blame him though.. I've always been bad at math

 

[Cosmickarma]

<< And what's that dy/dx thing >>



are you kiddin or you dont know? how did you get out of high school ? which univ are u at? where the damn pardy at!!!!

 

[Ns1]

uh just FYI, if you don't know your derivitaves, you might as well drop out of calculus now, cuz calculus keeps building ^_^

 

[LuDaCriS66]

<<

<< And what's that dy/dx thing >>



are you kiddin or you dont know? how did you get out of high school ? which univ are u at? where the damn pardy at!!!! >>



I'm not kidding.. and I'm not out of high school. This IS high school calculus.. pretty sad huh

 

[LuDaCriS66]

<< uh just FYI, if you don't know your derivitaves, you might as well drop out of calculus now, cuz calculus keeps building ^_^ >>



No kidding... but I need the credit so I better work my ass off in this class.. I really need a tutor soon

 

[JohnnyReb]

Sorry, I assumed this was a college freshman question.

It may be that your teacher doesn't teach very well.

I still recommend a tutor, but for your test, go back to the textbook and take it one page at a time. Don't hurry and don't panic. Rework each problem, and every example until you "get" it. If you don't get it before the test, don't worry there either. Keep studying on your own (every night) and you WILL master basic calculus. It will just be a matter of hard work. If you finish the semester strong, your teacher will take that into accout for the grade.

Since math is a weak point for you, you are going to have to work harder than everyone else.

First thing, get off ATOT and stay off until you have a B in that class.

John

 

[Cosmickarma]

glad ur still in high school....i thought this was the begining of the demise of the us...

if your dad or mom went to college for an engineering degree, im sure they will be able to help you with dy/dx and some basic stuff like that...there are a lot of good guides out there on the internet..i suggest you learn a few rules of calculus, even if you dont understand them properly,blindly learn a few rules and then go through as many worked out examples of calculus related to your syllabus as you can. once you understand how it works , you will also get a better understanding of the rules and calculus...hope this helps.

 

[RaynorWolfcastle]

did your teacher explain what derivatives are? I mean the limit definition of a derivative. You may want to look that over, it's pretty intuitive if it's explained graphically.

The derivative rules are pretty much self-explanatory as to when to use them eg, when two functions are multiplied, you use the product rule; when it's a division, use the quotient rule etc...

here's a little trick my calc 1 teacher told us to remember the quotient rule (say it out loud or in your head, and write as you say it): low-d-high minus high d-low over low square. In other words, the function on the top of the division is called high, and the one on the bottom is called low.

Hope this helps

-Ice

 

[LuDaCriS66]

<< Sorry, I assumed this was a college freshman question.

It may be that your teacher doesn't teach very well.

I still recommend a tutor, but for your test, go back to the textbook and take it one page at a time. Don't hurry and don't panic. Rework each problem, and every example until you "get" it. If you don't get it before the test, don't worry there either. Keep studying on your own (every night) and you WILL master basic calculus. It will just be a matter of hard work. If you finish the semester strong, your teacher will take that into accout for the grade.

>>



Thanks for the tips. I'll have to give up my social life to do well at all in this class.. but I definately need to work on it the way you explained. Alright.. off to work thanks

 

[LuDaCriS66]

<< glad ur still in high school....i thought this was the begining of the demise of the us...

if your dad or mom went to college for an engineering degree, im sure they will be able to help you with dy/dx and some basic stuff like that...there are a lot of good guides out there on the internet..i suggest you learn a few rules of calculus, even if you dont understand them properly,blindly learn a few rules and then go through as many worked out examples of calculus related to your syllabus as you can. once you understand how it works , you will also get a better understanding of the rules and calculus...hope this helps. >>



Both my parents were born out of the country and didn't get much of an education so they can't help me whatsoever. I'll just need to see what i can do about getting a tutor. Thanks for your help

 

[LuDaCriS66]

<< did your teacher explain what derivatives are? I mean the limit definition of a derivative. You may want to look that over, it's pretty intuitive if it's explained graphically.

The derivative rules are pretty much self-explanatory as to when to use them eg, when two functions are multiplied, you use the product rule; when it's a division, use the quotient rule etc...

here's a little trick my calc 1 teacher told us to remember the quotient rule (say it out loud or in your head, and write as you say it): low-d-high minus high d-low over low square. In other words, the function on the top of the division is called high, and the one on the bottom is called low.

>>



He did teach that part of the chapter but I never fully understood it. I just have to read and try to do the whole chapter by myself for now since my teacher is of little help. Thanks for the help though. I'll try to remember that quotient rule thing

 

[dullard]

<< I'll try to remember that quotient rule thing >>



First thing to do is get rid of stupid excess rules. If you have a hard time remembering them all - then don't try. Just learn the ones you need. The quotient rule is one rule that is not needed. Why? Since every division is just a multiplication:

(x+5) / (x^2) = (x+5) * (1/x^2) = (x+5) * (x^-2)

Now you never need to memorize the quotient rule since you can turn all divisions into a multiplication. I swear I hear so many people complaining that they have to memorize 10 different math techniques - then I see that all 10 do the same thing and only one is ever needed... Math teachers are quite bad at teaching sometimes.

 

[RaynorWolfcastle]

<<

<< I'll try to remember that quotient rule thing >>



First thing to do is get rid of stupid excess rules. If you have a hard time remembering them all - then don't try. Just learn the ones you need. The quotient rule is one rule that is not needed. Why? Since every division is just a multiplication:

(x+5) / (x^2) = (x+5) * (1/x^2) = (x+5) * (x^-2)

Now you never need to memorize the quotient rule since you can turn all divisions into a multiplication. I swear I hear so many people complaining that they have to memorize 10 different math techniques - then I see that all 10 do the same thing and only one is ever needed... Math teachers are quite bad at teaching sometimes. >>



Usually I'd agree with you, but in this case, the rule is so easy to remember.... This way it is faster to apply than using the multiplication thing and chances of error are minimal

-Ice

 

[kaesile]

<< What the heck is the difference between all those rules?? The product rule, quotient rule, power rule, the sum and difference rule, and the chain rule. Also there's implicit differentiation.

How am I supposed to know when to use which rule?? You can see how lost I am.

And what's that dy/dx thing? Ah geez.. I'm so screwed. >>



If you haven't taken pre-calculus yet, then I would say try taking that first. Otherwise, it should have placed some sort of foundation for you to get to calculus - limit definition of a derivate, for example.

All those rules are designed to help you take derivatives without needing to do it the long way (with the limit definition). Each is applied for a different expression type. To take the derivative (with respect to x) of x^2, you don't use a hard-and-fast-rule, you just say that it's 2x. However, if it were something like (x+1)(x-3), you COULD use the product rule here, instead of multiplying it out. I know it's not as efficient, but it might be a good idea to try it, just to make sure you get the hang of it. Then, multiply the thing out first, and then take a convential derivative. They should be equal.

Quotient rule would be for something like (x+1)/(x^2 + 3).
Power rule... oh, sorry, was d[x^2] power rule? I forget. Well, then that might be the power rule, but I can't remember for sure. Moving on...
Skip that... Skip that... (sorry, can't remember the names for all of these - I'm very bad at memorizing the 'names' of the rules)
Chain rule is for when you have a function of a function - something like sin(x^2). You know that derivative of sin(x) is cos(x), but what about sin(x^2)? Here, you need the chain rule, so the answer is cos(x^2) * 2x.

Implicit differentiation, IMO, sucks, since you have some screwed up equation with x's and y's all over the place, and you can't solve it in terms of y OR in terms of x. Thus, you are forced to implicitly differentiate, which involves taking each term individually and differentiating it. I think.

And finally, dy/dx just means take the derivative of the function y in terms of x. For instance, if y = x^2, then dy/dx is 2x. Mathematicians just really like to use a lot of different notations for the same thing. I've also seen d/dx, and also y'.

If you like history, I think the reason this happened was because calculus was developed independently at the same time (Newton and Liebniz, I think), and different people used different notation to do the same thing.

Other than that, I think what other people have said about general math study is good... Just work hard at it, and getting a tutor is also a good idea. Study groups are also useful.

 

[LuDaCriS66]

Thanks to everyone that helped. I really really appreciate all the time you guys put into explaining this stuff to me.

I just have one question.. for now

Find an equation of the tangent line to the curve at the given point.

y= 1 / x^2 + 1 , (-2, 1/5)


Now when I work it out with the quotient rule, I get -2x / (x^2 + 1)^2. When I substitute -2 for x, I get 4/25. But the question asks for an equation... how would I work that out from the answer? It should be really simple.. I'm just not too sure on this. I've been studying every chapter on derivatives for the past few hours.. but I still don't understand some of the simplest things math dunce..

thanks

 

[dullard]

<< Find an equation of the tangent line to the curve at the given point.

y= 1 / (x^2 + 1) , (-2, 1/5)

Now when I work it out with the quotient rule, I get -2x / (x^2 + 1)^2. When I substitute -2 for x, I get 4/25. But the question asks for an equation >>


You got through all the calculus - now you need to do some algebra. The equation of a line is often given by:

y = slope * x + constant

So in your case it becomes:

y = 4/25 * x + constant

Plug in your given point for y and x:

1/5 = 4/25 * -2 + constant

Solve for the constant:

constant = 1/5 + 4/25 * 2 = 13/25

Thus your equation is:

y = 4/25*x + 13/25

 

[LuDaCriS66]

Thanks a lot! I never knew you had to bring that slope equation into it. I guess you have to use it everytime you're looking for the equation in a question like this?

Thanks again!

 

[RaynorWolfcastle]

an even simpler way to express it would be 4/25 = (y - 1/5) / (x + 2), no calculation or algebra required!

-Ice

 

[dullard]

<< I guess you have to use it everytime you're looking for the equation in a question like this? >>



Your original question, "Find an equation of the line" shows that you need to do something similar to what I did. Anytime you need to find an equation of a line, you must use that equation (or something equivalent). There are an infinite number of ways to write that same equation, but I wrote what I thought was the most simple to me. Your algebra teacher may have shown you another form - use whichever one you like the best. Icecool83 showed a different form than I did. His method is quite useful in this case, but less useful in other cases. So our school system tries to teach 10 methods to do the same exact thing...leading to confused students. Use whichever one you like the best and ignore all other methods.

The problem that I see far too often is that people can do the calculus just fine (like you did). But then they don't know how to continue with the algebra (they then often complain that Calculus is hard - when in reality it is the algebra that is tricky for most students). I don't know what our education system did to teach algebra so poorly. Our math education needs a serious overhaul.

 

[LuDaCriS66]

<<

<< I guess you have to use it everytime you're looking for the equation in a question like this? >>





The problem that I see far too often is that people can do the calculus just fine (like you did). But then they don't know how to continue with the algebra (they then often complain that Calculus is hard - when in reality it is the algebra that is tricky for most students). I don't know what our education system did to teach algebra so poorly. Our math education needs a serious overhaul. >>



Hey that's 100% true. For this derivative work, the calculus part is pretty easy once I got the hang of it and knowing which rule to use at what times.... but the algebra really confused me. Especially the questions with square roots and where you have to multiply the top and bottom with that square root. Thanks for your help again

 

[poohhairt]

I'm in high school AP Calc right now too. I'm not sure if you have anything like this now, but here's a link for two very helpful cheat sheets. One is a derivative sheet, listing the derivatives of common things like trig functions, logs, etc. It also has the quotient rule, product rule, chain rule, and all those fun things. The other is a trig identity sheet, which can also come in handy.

Calculus Page at MHS

BTW: If anyone can help with the extra credit problem posted there, I would be very greatful!

-Aaron

 

[dullard]

<< Especially the questions with square roots and where you have to multiply the top and bottom with that square root. >>



Ahh the picky math teacher syndrome. I had one of those too. There is no logical reason to move the square root to the top:
A) It takes more work,
B) The final equation is much larger (less simple) if you move it to the top,
C) Calculators can easily divide by a square root,
D) Many times if the square root starts on the bottom, your future work will be much simplified if you keep it on the bottom.

That started back before there were calculators. Books with math tables and sliderules could give you a square root answer in the numerator only. Thus math people decided to create a standard that moved the square root to the top. Now that calculators can divide by a square root - there is no reason to keep this old legacy practice around.

So deal with it since you have a picky teacher. Then in real life - realize that there is no reason to do that anymore.