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How do you work out this differentiation???

Hi guys

So I have been self teaching myself Calculus and have got to (what I think) is one of the more tricky questions.


Could somebody please answer the queston below and pleeeeeeaaaase show ALL of your working!

I have some vague working out but would just like to compare it to a correct answer!


Please someone

1410860559694.jpg1410860559694.jpg

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Original post by lewif002
Hi guys

So I have been self teaching myself Calculus and have got to (what I think) is one of the more tricky questions.


Could somebody please answer the queston below and pleeeeeeaaaase show ALL of your working!

I have some vague working out but would just like to compare it to a correct answer!


Please someone


Which differentiation technique would be best to use - chain rule, quotient rule or product rule?
Original post by lewif002
Hi guys

So I have been self teaching myself Calculus and have got to (what I think) is one of the more tricky questions.


Could somebody please answer the queston below and pleeeeeeaaaase show ALL of your working!

I have some vague working out but would just like to compare it to a correct answer!


Please someone

1410860559694.jpg1410860559694.jpg


You seem to have jumped from not understanding the basics at the weekend to differentiating quotients


Could you show some working out
What rule have you applied - the product rule with negative indices or the quotient rule?
Reply 3
Avatar for lewif002
lewif002
OP
16
Original post by TenOfThem
You seem to have jumped from not understanding the basics at the weekend to differentiating quotients


Could you show some working out
What rule have you applied - the product rule with negative indices or the quotient rule?


I have used the quotient rule I believe. Please correct me if I am wrong (on anything)

You are such a great help TenOfThem, thank you in advance


EDIT - Sorry my attachments keep showing up sideways :angry:
1410862255355.jpg277.6KB
Original post by lewif002
I have used the quotient rule I believe. Please correct me if I am wrong (on anything)

You are such a great help TenOfThem, thank you in advance


EDIT - Sorry my attachments keep showing up sideways :angry:


Your differentiating is ok

the 4x should be -4x

the denominator has lost its square
Reply 5
Avatar for lewif002
lewif002
OP
16
Original post by TenOfThem
Your differentiating is ok

the 4x should be -4x

the denominator has lost its square


Aha 2 small errors on my behalf. Other than this is the answer correct?
Original post by lewif002
Aha 2 small errors on my behalf. Other than this is the answer correct?


yes
Reply 7
Avatar for lewif002
lewif002
OP
16
Original post by TenOfThem
yes


Brilliant thank you

One question I have had pecking at my brain is the following:

How is the derivative of any integer always 0?!
I understand that its correct and because it has no slope on a graph etc BUT if you apply normal differentiation to a whole number it works out like this...

Example f (x) = 5

So to differentiate it turns in to...

1x5^0 ... 5^0 = 1 so 1x1 is 1???

I understand the correct answer is actually zero

Just trying to get some understanding on the situation
Check out how to use latex dude.
It will your questions and life here in the forum much easier and beneficial. For Mathmos it is essential.



http://www.thestudentroom.co.uk/wiki/LaTeX
Original post by lewif002
Brilliant thank you

One question I have had pecking at my brain is the following:

How is the derivative of any integer always 0?!
I understand that its correct and because it has no slope on a graph etc BUT if you apply normal differentiation to a whole number it works out like this...

Example f (x) = 5

So to differentiate it turns in to...

1x5^0 ... 5^0 = 1 so 1x1 is 1???

I understand the correct answer is actually zero

Just trying to get some understanding on the situation


You are differentiating with respect to x
You are not interested in the power of the 5

f(x)=5x0f(x) = 5x^0 is what you are actually differentiating
Original post by lewif002
Brilliant thank you

One question I have had pecking at my brain is the following:

How is the derivative of any integer always 0?!
I understand that its correct and because it has no slope on a graph etc BUT if you apply normal differentiation to a whole number it works out like this...

Example f (x) = 5

So to differentiate it turns in to...

1x5^0 ... 5^0 = 1 so 1x1 is 1???

I understand the correct answer is actually zero

Just trying to get some understanding on the situation


There is no need to think of an integer being to a power of zero. An integer is not a function of any kind at all. It has no derivative and no effect on any derivatives. It is true to say it has a derivative of zero but that does not give an exact understanding. If you plot a function then add a constant and replot the shape and slope do not change.

I really admire how you are cracking on with this but going back a bit to using the definition of a derivative (and the notation) will really help you get to grips with it.
(edited 9 years ago)
Reply 11
Avatar for davros
davros
16
Original post by Old_Simon
There is no need to think of an integer being to a power of zero. An integer is not a function of any kind at all. It has no derivative and no effect on any derivatives. It is true to say it has a derivative of zero but that does not give an exact understanding. If you plot a function then add a constant and replot the shape and slope do not change.

I really admire how you are cracking on with this but going back a bit to using the definition of a derivative (and the notation) will really help you get to grips with it.


At the risk of sounding slightly picky, an integer (or any other constant) is a trivial function - whatever input you give it, it spits out the same value. Its derivative is trivially zero because if you plot this function on cartesian axes it is a horizontal line whose slope (which coincides with the tangent at any point) is 0.

(This is isn't directed at you, but I've seen students come on here before who've been told by their teacher that "a constant isn't a function" and this is patently untrue!)
Original post by davros
At the risk of sounding slightly picky, an integer (or any other constant) is a trivial function - whatever input you give it, it spits out the same value. Its derivative is trivially zero because if you plot this function on cartesian axes it is a horizontal line whose slope (which coincides with the tangent at any point) is 0.

(This is isn't directed at you, but I've seen students come on here before who've been told by their teacher that "a constant isn't a function" and this is patently untrue!)

The derivative dy/dx makes no sense if x is a constant because there is no x. Semantics and degree level maths aside this guy is self teaching calculus but has an idea that the power rule for x^n is the basis for differentiating constants. It is not.
Original post by Old_Simon
The derivative dy/dx makes no sense if x is a constant because there is no.


:confused:
Reply 14
Avatar for lewif002
lewif002
OP
16
Original post by Old_Simon
The derivative dy/dx makes no sense if x is a constant because there is no x. Semantics and degree level maths aside this guy is self teaching calculus but has an idea that the power rule for x^n is the basis for differentiating constants. It is not.


Would I be correct to assume x^n is the basis for differentiating everything other than constants?
Original post by BabyMaths
:confused:

We can not differentiate y with respect to x unless we have a function of x to start with. Where y equals a constant k there is no function. y never changes because there is no x which changes. Thus it is not exact to say the derivative of a constant is zero. In fact a constant k has no derivative at all.
Mathematically that is expressed as zero.
Original post by lewif002
Would I be correct to assume x^n is the basis for differentiating everything other than constants?


No

You can differentiate any function of x

Sin(x)
ln(x)

etc
Reply 17
Avatar for Dijonnay
Dijonnay
Isn't that the quotient rule formula you use?
Original post by lewif002
Would I be correct to assume x^n is the basis for differentiating everything other than constants?

No. The power rule lets us diff x^n and that is it. (including fractional and negative exponents).

Where y equals x, ax or k those are different cases.
Somebody tell me wtf differentiation is and why it works so perfectly.

Thx

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