Don't worry, I saw where you were coming from, went back, and reviewed. I made sure I understood how to derive the rules, and how to use the difference quotient to find a derivative.
The quiz was a success; as for the rest of the class, well, I probably need to get some of my shit together still, but it could be a lot worse.
Let me help you.Thisis the Chain Rule.Thisis the Product Rule. Can you see where you used the Product Rule instead of the Chain Rule?
I used the chain rule when deriving the first derivative. I then used a combination of the chain and product rule when deriving the second derivative.
You don't know the difference between the Chain Rule and the simple rule for the derivative of sin(x). You got the derivative of the angle function when you had to calculate du/dx. That might look like the Chain Rule to you, but it's not. Sorry.
It's odd that you went back and edited your posts right after I told you that you were wrong then. I guess it was just coincidence, huh?
Believe it or not (in your case, you won't), I was constantly editing my posts without looking for your replies (until I felt satisfied with the current post I was editing). All of the posts I made in this thread where I was working on the equations were edited roughly 10-20 times each. There was one point where I left my equations with cosine instead of sine, and the only thing you said was wrong about it was "-1 for not factoring". You didn't even point out that I goofed and wrote cos instead of sin (in b4 "you just didn't know the correct derivative!").
Like you said above, Slick, you were editing your posts like mad. I went back and erased the bit where I said you differentiated cos wrong because you had already changed it and anyone else reading later wouldn't have seen cos differentiated correctly and then me saying that it hadn't been. That's why lots of people don't edit their posts so much - as a courtesy to others so that they don't feel that they have to edit their posts as well.
I go to a private school . . .
I never would have guessed that someone as whiny, petulant, and obviously spoiled as you went to private school. Interesting.
You might have made a good grade in whatever your school calls Pre-Calculus, but by your own admission, your grade is slipping and you don't know how to differentiate trig functions well. Judging from this thread, you'll be lucky not to fail this quarter.
However, trying to use them without proving them first, as many high school students tend to do, turns calculus into mostly pattern recognition. This may make things easier in the short term, but means that you will go into university-level classes lacking some important tools, especially if you plan on using the AP exam to avoid retaking the class.
That's exactly what I was trying to say, but expressed much more artfully. The thing Dong doesn't understand is that he's both too tied up trying to make people think he's smarter than his teachers and too lazy to actually do the work to understand what he's doing in Calculus to really be credited with learning anything more than jumping through hoops.
HungryJoe: That grade looks like it is for a calculus class, not precalculus. Also, you are judging him much too harshly due to your own assumptions about his motives. Lots of people make mistakes the first time they learn new material. If he had taken and passed a calculus class without being able to take the derivative you gave, then that would be troubling, but he is a few months into a high-school level class. It's not unreasonable that he doesn't know how to do it yet.
What does bother me is the order of topics in the textbook he's using. Unless they have one hell of a pre-calc program, it seems like the textbook itself is setting the students up to only learn the cookbook approach to calculus.
Yes, it does say Calculus, but I'll bet the course material is really PreCalculus. It kinda reminds me of a thread from a few months ago where some idiots thought you would need Calculus to solve a quadratic equation.
I've encountered that "cookbook" approach before. You can teach kids in grammar school to use the Power Rule, but they don't really know what they're doing.
OK kids, settle down. (Though I'm somewhat pleased that one of the most heated threads in the forum concerns calculus).
I can say this, however. These sorts of derivations are definitely precalculus-level. You should be able to handle all standard derivatives semi-intuitively and without resorting to memorized rule sets (unless you understand from where said rulesets derive), or else you're going to be completely, utterly screwed when you get to the real parts of calculus (integration and beyond).
Derivatives are the easy part. Take the time to fully understand what it is that you're doing. Do things the long way. Derive the rules yourself. Engage in some trial and error. Show your work. Don't skip steps unless you understand exactly what all those steps are really doing.
Of course, that's all moot if you don't already have an intuitive grasp of trigonometric functions: you kind of need to already be proficient with them in all of their simple forms before you can really understand their derivatives and what they mean.
Also, learn to factor. Being able to factor complex blobs quickly in your head will be more useful to you than you can imagine in later maths.
As a last piece of advice (though this will be more useful in diffEQ and integration): whenever you're stuck, multiply both sides of an equation by one. You can almost always make a complex problem more simple by multiplying by one.
That might look like the Chain Rule to you, but it's not. Sorry.
Sure, Dkong didn't write out the specifics in full (though that is wholly unnecessary for such a simple question), but he did use the Chain Rule. In the first step of what he posted, he essentially did the following:-
Apart from this, however, Dkong is completely wrong and HungryJoe is right
That might look like the Chain Rule to you, but it's not. Sorry.
Sure, Dkong didn't write out the specifics in full (though that is wholly unnecessary for such a simple question), but hediduse the Chain Rule.
I seriously doubt that he did that. He looked at what his book told him to do to differentiate sin(u) and wrote cos(u)(du/dx) and then wrote cos(2x3)(6x2). He understands the Chain Rule like Sarah Palin understands the role of the VP.
True, perhaps he really did not know that he was using the Chain Rule, but that is nonetheless what he did, in effect
I do understand the Chain rule and how it works. I knew I was using the Chain Rule when I was working out HungryJoe's problem. But before I consulted my textbook, I was unsure if I had to use the Chain Rule or Product Rule to get the derivative of sin(2x3). Yes, quite a noob move, especially coming from someone in AP Calculus...but shit happens, I guess.
I never would have guessed that someone as whiny, petulant, and obviously spoiled as you went to private school. Interesting.
It's just a Catholic School. Not everyone that goes here is rich, they give out financial aid if need be. I'm not so sure what image popped into your mind when I said "private school", but my school isn't some snooty school where everything is fancy and you have to wear suits and shit. Not even close. Also, the stereotype that whiny and spoiled kids go to private schools is dumb. There are spoiled kids at public school. There are non-spoiled kids at my school.
You might have made a good grade in whatever your school calls Pre-Calculus, but by your own admission, your grade is slipping and you don't know how to differentiate trig functions well. Judging from this thread, you'll be lucky not to fail this quarter.
It's AP Calculus BC (the "HN" part was denoting that we get honors credit for the class, meaning it's out of a 5 point gpa scale). Also, I just aced a few more of the daily quizzes. I'd be lucky to receive an A+, but likely to receive an A, seeing as the quarter ends on Friday.
What does bother me is the order of topics in the textbook he's using.
This is the book we're using. You can go on that site and look at the order of the topics. You can look at what each chapter is and what is taught (and the order it's in) in each chapter. We're just finishing up chapter 3.
In the meantime, I'd like to see him differentiate xx
I've never had to do a problem like that before...how would you do that?
I'm relatively glad, now, that I took the time to learn how to derive those rulesets...We started doing higher derivatives today (among other things) and I was like, "Oh mans, if I didn't do all that work I'd be totally in over my head by now." I did fine on the quiz, though, with my teacher noting that my difference quotient work was "perfect," so I seem to have that base covered.
On an unrelated note, I should probably go back and review analytic trig and "learn how to factor," as Rym put it. It would serve me well to review those two topics.
In the meantime, I'd like to see him differentiate xx
I've never had to do a problem like that before...how would you do that?
At least you realise that none of the usual methods actually apply here until you manipulate it into a different form. You convert it to the form ef(x) and differentiate that.
Sorry to be relatively off-topic, but holy cow, I'm gonna have to do this stuff? Ugh, it makes my head hurt... I should stop reading the 'smart topics.'
Sorry to be relatively off-topic, but holy cow, I'm gonna have to do this stuff? Ugh, it makes my head hurt... I should stop reading the 'smart topics.'
Well, strictly speaking, you don't have to do anything. You could just flip burgers for the rest of your life.
/doesn't remember a damn thing about calculus //doesn't care
Yep, based on stuff I said on a web forum, I'm sure you understand every facet and personality trait of me and can label me a spoiled kid with 100% certainty. Frankly, I don't see how being a dick and not fully understanding calculus correlates to being spoiled. I mean, I can see petulant, and I can sort of see whiny, but I fail to see where you pulled spoiled.
Also, there's a line of courtesy, even on the 'net, and you've crossed it (actually you crossed it quite awhile ago). Yes I've been being a dick in this thread, but aside from telling you to suck my balls, I haven't made any personal attacks at you, or called you any names. You, on the other hand, stepped over that line a long time ago. It's getting ridiculous.
Sorry to be relatively off-topic, but holy cow, I'm gonna have to do this stuff? Ugh, it makes my head hurt... I should stop reading the 'smart topics.'
Well, strictly speaking, you don'thaveto do anything. You could just flip burgers for the rest of your life.
/doesn't remember a damn thing about calculus //doesn't care
But I would like to have my life have meaning of some sort. That, and I could flip burgers better with bloody arm-stubs than silly fast-food-burger-flippers could ever imagine. Unless they were pro burger flippers. Then I couldn't stand a chance in a flip-off.
The lesson continues, because I got bored and wanted more people to complain about Calculus so I could laugh at them. For the question I asked before, there are two essentially equivalent ways to go about it: 1. Re-arranging to the form ef(x), as I said before. 2. Implicit Differentiation
Implicit Differentiation is an important thing you will learn, though certainly only after you understand the difference quotient. You'll need it to differentiate the arctan function
Incidentally, this online equation editor that allows you to make equations in LaTeX and link them is awesome. Not as awesome as a LaTeX engine inbuilt into the forum, but that is wholly unnecessary here I guess.
But I would like to have my life have meaning of some sort. That, and I could flip burgers better with bloody arm-stubs than silly fast-food-burger-flippers could ever imagine. Unless they were pro burger flippers. Then I couldn't stand a chance in a flip-off.
So, assuming you flip better than anybody else and people tell their friends about your awesome flipping skills. Your business grows and you need to expand your business, but you don't know by how much. If you knew calculus and statistics you could easily figure it out but without them you rely on guesswork.
What I'm trying to point out here is that you don't just need calculus to get through college math and physics, you need calculus because in the real world it answers all the interesting questions.
/does integrals using a 1000 page Russian table of integrals
Incidentally, this online equation editor that allows you to make equations in LaTeX and link them is awesome. Not as awesome as a LaTeX engine inbuilt into the forum, but that is wholly unnecessary here I guess.
Incidentally, this online equation editor that allows you to make equations in LaTeX and link them is awesome. Not as awesome as a LaTeX engine built into a forum, but that is wholly unnecessary here I guess.
I remember I was really, really impressed with Wesley Clark when he said in the 2004 election primaries that one of the things he remembers well from school was how thrilled he was to understand how to differentiate . It's a shame he didn't win the nomination that year.
Thanks for the HTML lesson. TeX the world, though, only works if everyone is using it. I am just seeing some syntax jammed between brackets.
And is one heck of an equation. You could give individual lectures on the significance of each individual symbol and it's influence on mathematics. Negative numbers (implying the number zero), Pi, imaginary numbers and e are all related to major advances in science. Needless to say it is my favorite equation.
Comments
The quiz was a success; as for the rest of the class, well, I probably need to get some of my shit together still, but it could be a lot worse.
You might have made a good grade in whatever your school calls Pre-Calculus, but by your own admission, your grade is slipping and you don't know how to differentiate trig functions well. Judging from this thread, you'll be lucky not to fail this quarter. That's exactly what I was trying to say, but expressed much more artfully. The thing Dong doesn't understand is that he's both too tied up trying to make people think he's smarter than his teachers and too lazy to actually do the work to understand what he's doing in Calculus to really be credited with learning anything more than jumping through hoops.
That grade looks like it is for a calculus class, not precalculus.
Also, you are judging him much too harshly due to your own assumptions about his motives. Lots of people make mistakes the first time they learn new material. If he had taken and passed a calculus class without being able to take the derivative you gave, then that would be troubling, but he is a few months into a high-school level class. It's not unreasonable that he doesn't know how to do it yet.
What does bother me is the order of topics in the textbook he's using. Unless they have one hell of a pre-calc program, it seems like the textbook itself is setting the students up to only learn the cookbook approach to calculus.
I've encountered that "cookbook" approach before. You can teach kids in grammar school to use the Power Rule, but they don't really know what they're doing.
I can say this, however. These sorts of derivations are definitely precalculus-level. You should be able to handle all standard derivatives semi-intuitively and without resorting to memorized rule sets (unless you understand from where said rulesets derive), or else you're going to be completely, utterly screwed when you get to the real parts of calculus (integration and beyond).
Derivatives are the easy part. Take the time to fully understand what it is that you're doing. Do things the long way. Derive the rules yourself. Engage in some trial and error. Show your work. Don't skip steps unless you understand exactly what all those steps are really doing.
Of course, that's all moot if you don't already have an intuitive grasp of trigonometric functions: you kind of need to already be proficient with them in all of their simple forms before you can really understand their derivatives and what they mean.
Also, learn to factor. Being able to factor complex blobs quickly in your head will be more useful to you than you can imagine in later maths.
As a last piece of advice (though this will be more useful in diffEQ and integration): whenever you're stuck, multiply both sides of an equation by one. You can almost always make a complex problem more simple by multiplying by one.
/went to calculus parties in high school
In the first step of what he posted, he essentially did the following:-
Apart from this, however, Dkong is completely wrong and HungryJoe is right
In the meantime, I'd like to see him differentiate
xx
That should be more telling
Also, the stereotype that whiny and spoiled kids go to private schools is dumb. There are spoiled kids at public school. There are non-spoiled kids at my school. It's AP Calculus BC (the "HN" part was denoting that we get honors credit for the class, meaning it's out of a 5 point gpa scale). Also, I just aced a few more of the daily quizzes. I'd be lucky to receive an A+, but likely to receive an A, seeing as the quarter ends on Friday. This is the book we're using. You can go on that site and look at the order of the topics. You can look at what each chapter is and what is taught (and the order it's in) in each chapter. We're just finishing up chapter 3. I've never had to do a problem like that before...how would you do that?
On an unrelated note, I should probably go back and review analytic trig and "learn how to factor," as Rym put it. It would serve me well to review those two topics.
You convert it to the form ef(x) and differentiate that.
/doesn't remember a damn thing about calculus
//doesn't care
A math student could say that the intersection of the set of non-spoiled kids at your school and you is the null set.
I mean, I can see petulant, and I can sort of see whiny, but I fail to see where you pulled spoiled.
Also, there's a line of courtesy, even on the 'net, and you've crossed it (actually you crossed it quite awhile ago). Yes I've been being a dick in this thread, but aside from telling you to suck my balls, I haven't made any personal attacks at you, or called you any names. You, on the other hand, stepped over that line a long time ago. It's getting ridiculous.
Unless they were pro burger flippers. Then I couldn't stand a chance in a flip-off.
1. Re-arranging to the form ef(x), as I said before.
2. Implicit Differentiation
Implicit Differentiation is an important thing you will learn, though certainly only after you understand the difference quotient. You'll need it to differentiate the arctan function
Incidentally, this online equation editor that allows you to make equations in LaTeX and link them is awesome. Not as awesome as a LaTeX engine inbuilt into the forum, but that is wholly unnecessary here I guess.
What I'm trying to point out here is that you don't just need calculus to get through college math and physics, you need calculus because in the real world it answers all the interesting questions.
/does integrals using a 1000 page Russian table of integrals
Edit: Btw, all of you struggling to get to grips with trigonometry should look at
Makes stuff a lot easier to understand (and derive).
Edit: fixed borders as per Lack's suggestion.
He still has an impressive friendliness to science in this age where people like Palin are elected to high office knowing nothing about science or math at all.
Add border=0 to the img tags.
[;e^{\pi i} + 1 = 0;]
Also, use
style="border: 0;"instead ofborder="0"And
If we don't have enough math discussions, we should have more. Less invasions, more equations!