Quick Maths Question

[Ezeran]

I'm re-doing my higher maths for a uni course and I've got a test on the first set of stuff in a few days and I have most of it down fine but there's one question in a practice test I just can't get and it's annoying me no end. So figured theres bound to be someone far more maths able than me here.

Thje question is :
Given that y= 4x^2 - 3x over 2x^2 find dy/dx

Now I know I have to split it before I can differentiate but all my notes and things I can't find an example of splitting it when you have an x value on the upper half of the fraction and an x value with both a value before the x and an exponent.

Also can anyone remind me what the number before an x as in 4x is called again can't for the life of me remember.

 

[fade]

Short answer: use the quotient rule. (Could use the product rule, too.)

The number is called a coefficient.

EDIT: Here's the quotient rule, by the way:

 

[Overflight]

(4x^2-3x)/(2x^2)=(4x^2/2x^2)-(3x/2x^2)=2-(3/2x)=2-(3/2)x^-1

dy/dx = (3/2)*(-1)x^(-1-1)=(3/2)x^-2=(3/2x^2)

 

[Zonker]

Oh my god. Read the frickin manual! lol.

You haven't written the problem down rigorously, first of all, is it

y = (4x^2-3x)/(2x^2)? Then the x's cancel!

y = (4x-3)/2x = 2 - (3/2x)

Spoiler

and dy/dx = 3/2x^2, qed.

If it's

y = 4x^2 - (3x/2x^2) then that simplifies to
y = 4x^2 -(3/2x)

Spoiler

and dy/dx = 8x+3/2x^2

The 4 in 4x^2 is called a coefficient. The rule is, if a is a coefficient, then d(ax)/dy = a*dx/dy

 

[Overflight]

Oh my god. Read the frickin manual! lol.

y = (4x-3)/2x = 2 - (3/2)*x and dy/dx = - 3/2, qed.

y = 4x^2 - (3x/2x^2) then that simplifies to
y = 4x^2 -(3/2)x and dy/dx = 8x-3/2

Both these steps are incorrect: (3/2x) is NOT equal to (3/2)*x

 

[Zonker]

yeah yeah, frickin ninjas

 

[fade]

I wasn't going to do it for him.

 

[Zonker]

Good point. I should've stopped at pointing out that the x's cancel.

 

[Ezeran]

No thanks guys an example was exactly what I needed (also I wrote the question down wrong it was 4x^3 not ^2)

Right so now I have

y=(4x^3-3x)/2x^2=4x^3/2x^2-3x/2x^2=4x/2-3/2x=2x-3/2x=2x-3/2x^-1

dy/dx=2+3/2x^1=2+3/2x^2

That look about right?

Also yet again thanks for the help was exactly what I needed to get my head round this. Right now, provided that right, to track down an example or two in the same vein for further practice

 

[Soliloquy]

maths

That word just seems so weird to us Americans. It's like reading the word "grammars."

 

[fade]

It is uncomfortable. I guess can see it as an abbreviation of mathematics, but it's a subject, and plural feels wrong. Like "I'm taking biologies."

 

[LittleSin]

I have a math-phobia. I walked into this thread and the minute I saw the equation my brain seized up, my heart started beating hard, and my palms got sweaty.

I blame this on my dads ex-girlfriend...the one that used to beat me for funsies. She was a math teacher.

I really wish I could get over this fear. It makes day to day life difficult.

 

[Cajungal]

This thread makes me glad I'll never have to do anything much more complicated than teach kids arithmetic, telling time and maybe basic algebra.

 

[fade]

Math weenies.

 

[Ezeran]

Heh my issue with it is the same as my issue with anything if I get stuck and can't work something out pretty quickly I get more and more fustrated and can't sort it which is why I needed the example. Strangly this doesn't happen when I'm debugging code.

And also calling it just maths sounds equally weird to me it's always been maths to me and it always will.

In fact my text book I have here is called "Maths in Action"

 

[MindDetective]

It always makes me sad when people just write off math. As with all things, there can be joy in math and people are missing out on it. Heck, I wish I could remember calculus and I really would love to learn combinatorics and graph theory. It doesn't need to be scary or hard, really. It can be as enjoyable as doing a crossword puzzle, really. Unfortunately people are taught it is something they have to learn rather than something that is enjoyable to learn.

 

[Soliloquy]

It always makes me sad when people just write off math. As with all things, there can be joy in math and people are missing out on it. Heck, I wish I could remember calculus and I really would love to learn combinatorics and graph theory. It doesn't need to be scary or hard, really. It can be as enjoyable as doing a crossword puzzle, really. Unfortunately people are taught it is something they have to learn rather than something that is enjoyable to learn.

I've gotta be honest, I enjoyed taking two semesters of calculus, even though it wasn't required for my major (Journalism). I just wish I could remember how it worked, and (more importantly) what the heck all of those weird symbols they use mean.

This was an interesting refresher, though:

 

[Zonker]

No thanks guys an example was exactly what I needed (also I wrote the question down wrong it was 4x^3 not ^2)

Right so now I have

y=(4x^3-3x)/2x^2=4x^3/2x^2-3x/2x^2=4x/2-3/2x=2x-3/2x=2x-3/2x

or 2x-(3/2)*x^-1

dy/dx=2+3/2x^2 or 2+(3/2)*x^-2

That look about right?

Also yet again thanks for the help was exactly what I needed to get my head round this. Right now, provided that right, to track down an example or two in the same vein for further practice

cleaned up a bit for you

 

[fade]

I love math. I'm a physicist. I live in it everyday. I hate the way that it's taught, though. There's never an eye to what it means. Instead, it's taught as a set of rules. That makes it dry and difficult to understand. I mean, for instance, it's one thing to learn, say, the chain rule. Sure, it's an easy rule. But what does it mean? Why does it work that way? What is a derivative? Those questions don't get enough attention.

 

[Ross]

I love math. I'm a physicist. I live in it everyday. I hate the way that it's taught, though. There's never an eye to what it means. Instead, it's taught as a set of rules. That makes it dry and difficult to understand. I mean, for instance, it's one thing to learn, say, the chain rule. Sure, it's an easy rule. But what does it mean? Why does it work that way? What is a derivative? Those questions don't get enough attention.

This... only I'm a meteorologist.

 

[Ezeran]

I love math. I'm a physicist. I live in it everyday. I hate the way that it's taught, though. There's never an eye to what it means. Instead, it's taught as a set of rules. That makes it dry and difficult to understand. I mean, for instance, it's one thing to learn, say, the chain rule. Sure, it's an easy rule. But what does it mean? Why does it work that way? What is a derivative? Those questions don't get enough attention.

That could be the problem I have with it compared to say more complicated programming errors I've fixed, managed to reteach myself vectors in about a day and a half because I needed it for a program but this fairly basic differentiation problem caused me way too much hassle.

ah well only stationary points and recurrence relations to go and I'nm ready for my test

 

[Reboneer]

It is uncomfortable. I guess can see it as an abbreviation of mathematics, but it's a subject, and plural feels wrong. Like "I'm taking biologies."

Does "physics" sound weird to you?

 

[fade]

No, and neither does mathematics. But physs would.

 

[Wasabi Poptart]

It always makes me sad when people just write off math. As with all things, there can be joy in math and people are missing out on it. Heck, I wish I could remember calculus and I really would love to learn combinatorics and graph theory. It doesn't need to be scary or hard, really. It can be as enjoyable as doing a crossword puzzle, really. Unfortunately people are taught it is something they have to learn rather than something that is enjoyable to learn.

I did well in math until I took Algebra in 8th grade. We were given an exam at the end of the year. If you passed the exam with a certain score or higher, then you were allowed to go right into geometry in your freshman year. I missed it by one point. Passed the class, but had to retake Algebra as if I had failed the course. My relationship with mathematics quickly took a nosedive from there. I just started taking math classes again after 20+ years. I am amazed at how much I do understand now that I don't feel like I have to prove that I'm not a failure.

 

[Dieb]

I love math. I'm a physicist. I live in it everyday. I hate the way that it's taught, though. There's never an eye to what it means. Instead, it's taught as a set of rules. That makes it dry and difficult to understand. I mean, for instance, it's one thing to learn, say, the chain rule. Sure, it's an easy rule. But what does it mean? Why does it work that way? What is a derivative? Those questions don't get enough attention.

Math up through calculus is mostly boring. Memorize rules, as you say, plug in numbers, rinse and repeat. After calculus, however, it gets a lot more interesting. It's all about what things mean, and then proving that certain things are true. It's a shame most people drop out way before then.

Anyway, how derivatives work is fairly interesting. It's the slope of whatever equation you are taking the derivative of at a single point. The basic definition is it's the value of the limit as h approches zero of (f(x+h)-f(x))/h. This is just like caluculating a regular slope, which is the change in y divided by the change in x. h is the change in x, f(x+h)-f(x) is the change in y. However, as we want to know the slope at a single point, we take h and make it as close to zero as is possible (thus where the limit part of that equation comes from).

All the various rules (chain rule, quotient rule, etc) of derivatives can be proved from that definition.

 

[JONJONAUG]

I did perfectly in Math (got 800 on my Math SATs, As in classes, and all that jazz) until I reached Calc II last year.

Fuck integrals. Fuck them with a rusty spoon. Ended up with a C+ (which is REALLY fucking me up, since it was one of the courses I needed a B or above in to keep my scholarship and as prereqs for a few classes, so I've been sliding stuff around, taking a couple extra courses to make up for the "special honors section" course credit that I would've rather not have taken, and begging professors about taking their classes since then). And now because I can't take the "special honors section" of Statistics because of that grade and the C+ in this course doesn't count, I have to take a Web Design class.

Calc III on the other hand, wasn't all that bad. Calc I is astoundingly simple, you could probably learn all of the normal material taught in a Calc I class within a week if you were committed to it.

 

[Reboneer]

Anyway, how derivatives work is fairly interesting. It's the slope of whatever equation you are taking the derivative of at a single point. The basic definition is it's the value of the limit as h approches zero of (f(x+h)-f(x))/h. This is just like caluculating a regular slope, which is the change in y divided by the change in x. h is the change in x, f(x+h)-f(x) is the change in y. However, as we want to know the slope at a single point, we take h and make it as close to zero as is possible (thus where the limit part of that equation comes from).

All the various rules (chain rule, quotient rule, etc) of derivatives can be proved from that definition.

Is that not how most people are introduced to calculus?

 

[Zonker]

I was introduced to calculus by first being instructed to forget all math that I learned in high school. We methodically built the whole number system by making a series of assumptions about how we would expect numbers to behave, one at a time, and explored a number of properties you could prove based on those assumptions. Once we had the whole numbers we built the rational numbers using pairs of whole numbers, and then defined real numbers based on a convergence assumption we had to make for irrational numbers to exist. Once we had the real numbers we started exploring properties of functions and asking questions about how to solve certain problems. Eventually we made our way around to derivatives, and then integrals, but only after being forced to calculate the area under a curve without using Newton's little trick, by finding the convergence to a number of a series of rectangles drawn inside the area of the function.

So it was very hands-on and intuitive because every step logically sprung out of the previous steps we had taken, we proved everything conclusively to ourselves so we had no doubt that the tools we were using were true and we had an intuitive grasp of how and why they worked because we had worked through the proofs proving that they work.

Helped me because my actual calculating skills are pretty weak, but I have a good intuition for proofs, so I ended up as a math major even though I went to college thinking I'd be a creative writing major or something.

 

[fade]

Anyway, how derivatives work is fairly interesting. It's the slope of whatever equation you are taking the derivative of at a single point. The basic definition is it's the value of the limit as h approches zero of (f(x+h)-f(x))/h. This is just like caluculating a regular slope, which is the change in y divided by the change in x. h is the change in x, f(x+h)-f(x) is the change in y. However, as we want to know the slope at a single point, we take h and make it as close to zero as is possible (thus where the limit part of that equation comes from).

All the various rules (chain rule, quotient rule, etc) of derivatives can be proved from that definition.

Is that not how most people are introduced to calculus?[/QUOTE]

It is and it isn't. I mean, the teacher says that, but it's a rare teacher that doesn't gloss over that or attempt to make it intuitive before jumping into rules. Same with integrals. Sure, you get Riemann sums the first lecture, but you rarely hear from them again.

Let me give you an example. In my grad classes, I've consistently had the same reaction when I derive an integral from first principles for a bunch of geologists who haven't touched math since Calc II. Seeing it build from something finite always helps. The lights come on when you tell them that making the pieces smaller makes the sum an integral---after all, that integration symbol is just a giant "S" for "sum".