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# Differentiation

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1. A curve has equation y = 2x3 + x2 - 8x + 3.
Find dy / dx
Hi

Can someone please guide me through answering the above question step by step?

Thanks.
2. (Original post by _Xenon_)
A curve has equation y = 2x3 + x2 - 8x + 3.
Find dy / dx
Hi

Can someone please guide me through answering the above question step by step?

Thanks.
We need to know what you know already.

Do you know how to find if ?
3. (Original post by _Xenon_)
A curve has equation y = 2x3 + x2 - 8x + 3.
Find dy / dx
Hi

Can someone please guide me through answering the above question step by step?

Thanks.
http://m.wikihow.com/Differentiate-Polynomials
4. (Original post by notnek)
We need to know what you know already.

Do you know how to find if ?
Is it the power times by 2x (because there's a number in front of it)?

So 3 times by 2x , I can't remember the rest
5. (Original post by _Xenon_)
Is it the power times by 2x (because there's a number in front of it)?

So 3 times by 2x , I can't remember the rest
3 times by 2x then subtract 1 from the exponent
6. (Original post by notnek)
We need to know what you know already.

Do you know how to find if ?
By the way, we have not been taught this in school due to time so I'm learning some of the content myself hence the question as I'd like someone to expalin how these questions are done. :-)
7. (Original post by _Xenon_)
Is it the power times by 2x (because there's a number in front of it)?

So 3 times by 2x , I can't remember the rest
You're nearly there. Next you need to subtract one from the power.

So the 3 becomes a 2 :

Now do you have an idea how to differentiate ?

It looks like you need to over the basics of this topic by looking at your textbook / internet.
8. (Original post by _Xenon_)
By the way, we have not been taught this in school due to time so I'm learning some of the content myself hence the question as I'd like someone to expalin how these questions are done. :-)
Ignore the end of my last post - you need to go over the basics.

Can you tell me what you get if you differentiate these?

9. (Original post by notnek)
Ignore the end of my last post - you need to go over the basics.

Can you tell me what you get if you differentiate these?

I times by the power and reduce the power by one, right?

1.) 6x
2.) 24x^3
3.) 10x^4
10. (Original post by _Xenon_)
I times by the power and reduce the power by one, right?

1.) 6x
2.) 24x^3
3.) 10x^4
Correct

Now see if you can try these - they're a bit different

1)
2)
11. (Original post by notnek)
Correct

Now see if you can try these - they're a bit different

1)
2)
OK I'm guessing these using what I already know...

1.) 5x = 5x^1 = 5x^0 = 1
2.) 3 = 3^1 = 3^0 = 1

Are they both 1? Not sure...
12. (Original post by _Xenon_)
OK I'm guessing these using what I already know...

1.) 5x = 5x^1 = 5x^0 = 1
2.) 3 = 3^1 = 3^0 = 1

Are they both 1? Not sure...
is not equal to 1.

For the second one . Now try differentiating

I have to go out now but hopefully someone else will help you.
13. (Original post by _Xenon_)
OK I'm guessing these using what I already know...

1.) 5x = 5x^1 = 5x^0 = 1
This is almost correct. Think about is, what is 5x^0.

2.) 3 = 3^1 = 3^0 = 1

Are they both 1? Not sure...
This one, not so much. Remember, if you're differentiating w.r.t. (i.e you're doing then you only change the exponents of . 3 is not x.

So, we have, actually that: . So what's ?

Hint:
Spoiler:
Show
It's a nice round number.
14. (Original post by notnek)
is not equal to 1.

For the second one . Now try differentiating

I have to go out now but hopefully someone else will help you.
OK thanks I thought that because anything to the power of 0 was meant to be equal to 1. However, is just x^0 equal to 1? So is it 5 times by 1 which equals 5? Not sure...

(Original post by Zacken)
This is almost correct. Think about is, what is 5x^0.

This one, not so much. Remember, if you're differentiating w.r.t. (i.e you're doing then you only change the exponents of . 3 is not x.

So, we have, actually that: . So what's ?

Hint:
Spoiler:
Show
It's a nice round number.
OK so 3=3x^0 so is that 3*1 which equals 3??!
15. (Original post by _Xenon_)
OK thanks I thought that because anything to the power of 0 was meant to be equal to 1. However, is just x^0 equal to 1? So is it 5 times by 1 which equals 5? Not sure...
5 times 1 which equals 5, yes.

OK so 3=3x^0 so is that 3*1 which equals 3??!
Not, quite. Remember - you bring the power down, so for example: becomes
16. (Original post by _Xenon_)
OK I'm guessing these using what I already know...

1.) 5x = 5x^1 = 5x^0 = 1
2.) 3 = 3^1 = 3^0 = 1

Are they both 1? Not sure...
Just a quick point. From what you've written it looks like you're saying that 5x^1 = 5x^0, where you mean .
17. Okay, here are some rules that you should get used to for differentiating. What is is a linear operator. It's read as "the derivative of y with respect to x". Because it's linear, it's a very easy and nice operator.

So, we have, intuitively:

All this is saying that if you want to differentiate the sum of two (or more!) terms, you can differentiate each term separately and then add them together.

So, for example - you know that when you differentiate , you get . So if you were to differentiate you can simply write and then it follows that . Which makes sense!

Following on from that rule, it follows just as intuitively that

.

That is, if you want to differentiate a constant multiple of , you can pull the multiple out, differentiate the x term and then put the constant back in. This makes total sense for differentiating because we can do just like last time!

Now, you've just learnt that if you want to differentiate raised to a power, you do this:

i.e: all you need to do is multiply the entire thing by the power and then subtract 1 from the power. Do you understand this? Please tell me if you don't!

With these three rules, you can differentiate pretty much anything! How cool is that?!

If you want to differentiate a polynomial, you just differentiate each term separately and then add them up together.

So - for example, if you want to differentiate , I'd advise you to do this one step at a time (for now, once you get the hang of it, you can skip steps).

But for now, I want you to do something like this:

Please point out anything that you didn't understand in here.

Can you do these for me:

18. (Original post by Zacken)
5 times 1 which equals 5, yes.

Not, quite. Remember - you bring the power down, so for example: becomes
Hi is it 3*0= 0
19. (Original post by _Xenon_)
Hi is it 3*0= 0
Nopes, that's very correct.

The derivative of a constant is 0.

BTW, I've written up a post for you up there, read it, take a while to digest and understand what I've said, and then shower me with questions.
20. (Original post by Zacken)
Nopes, that's very correct.

The derivative of a constant is 0.

BTW, I've written up a post for you up there, read it, take a while to digest and understand what I've said, and then shower me with questions.
Ah so was the answer: 0x^-1
Thanks very much...

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