It’s been a while since I’ve used the chain rule. Applying the chain rule when there’s only one composite function is pretty straight forward but this question has multiple terms.

See below:

Regarding the letters I use to give the split the functions, does what I wrote make sense?

See below:

Regarding the letters I use to give the split the functions, does what I wrote make sense?

(edited 3 months ago)

Hmm... what you've written down is correct (though I'd suggest you to just skip all the fuss and just write the last two lines). What are you unclear of?

The strategy to differentiation in general is to (i) differentiate term by term; then (ii) use chain rule if needed. This is supposed to be a mechanical process.

The strategy to differentiation in general is to (i) differentiate term by term; then (ii) use chain rule if needed. This is supposed to be a mechanical process.

Original post by tonyiptony

Hmm... what you've written down is correct (though I'd suggest you to just skip all the fuss and just write the last two lines). What are you unclear of?

The strategy to differentiation in general is to (i) differentiate term by term; then (ii) use chain rule if needed. This is supposed to be a mechanical process.

The strategy to differentiation in general is to (i) differentiate term by term; then (ii) use chain rule if needed. This is supposed to be a mechanical process.

The faff is important to show the understanding as it’s for a course I’m doing. Without the faff showing how I found the answer, there’s nothing to suggest that I just found the answer online and copied it.

Original post by KingRich

The faff is important to show the understanding as it’s for a course I’m doing. Without the faff showing how I found the answer, there’s nothing to suggest that I just found the answer online and copied it.

Fair. If that's required by your course, then do show your steps.

I tend not to show this level to detail, as differentiating stuff is supposed to be trivial and uninteresting, and putting that much detail only confuses people.

Original post by KingRich

The faff is important to show the understanding as it’s for a course I’m doing. Without the faff showing how I found the answer, there’s nothing to suggest that I just found the answer online and copied it.

If you feel you need to do it, fine, but be aware that if you just need the derivative you "should" be able to write down $\dfrac{dV}{dx} = \cot x - 10(x^4-3x)^9(4x^3 -3)$ without needing intermediate steps.

On the other hand, if you do need to show your working to that extent, I think I should say that I find the way you write things out very confusing, with pieces of calculation appearing at semi-arbitrary places on the page with little connection between the pieces. A mathematical argument should flow from step to step - it shouldn't be necessary for me to search the page trying to work out how two pieces of calculation are connected.

If I had to give that level of working, I would probably go:

$V(x) = \ln(\sin(x)) - (x^4-3x)^{10}$. Write $p = \sin(x), q = \ln(p), r = x^4 - 3x, s = r^{10}$.

Then $V(x) = q - s$ and $\dfrac{dV}{dx} = \dfrac{dq}{dx} - \dfrac{ds}{dx}$. By the chain rule, the RHS equals $\dfrac{dq}{dp}\dfrac{dp}{dx} - \dfrac{ds}{dr}\dfrac{dr}{dx}$.

We now calculate these 4 terms:

$\dfrac{dp}{dx} = \cos(x), \dfrac{dq}{dp} =\dfrac{1}{p} = \dfrac{1}{\sin x}$

$\dfrac{dr}{dx} = 4x^3-3, \dfrac{ds}{dr} = 10 r^9 = 10(x^4-3x)^9$.

Substituting these in, we find that the RHS = $\dfrac{1}{\sin x} \cos(x) - 10(x^4-3x)^9(4x^3-3)$

(edited 3 months ago)

Original post by DFranklin

If you feel you need to do it, fine, but be aware that if you just need the derivative you "should" be able to write down $\dfrac{dV}{dx} = \cot x - 10(x^4-3x)^9(4x^3 -3)$ without needing intermediate steps.

On the other hand, if you do need to show your working to that extent, I think I should say that I find the way you write things out very confusing, with pieces of calculation appearing at semi-arbitrary places on the page with little connection between the pieces. A mathematical argument should flow from step to step - it shouldn't be necessary for me to search the page trying to work out how two pieces of calculation are connected.

If I had to give that level of working, I would probably go:

$V(x) = \ln(\sin(x)) - (x^4-3x)^{10}$. Write $p = \sin(x), q = \ln(p), r = x^4 - 3x, s = r^{10}$.

Then $V(x) = q - s$ and $\dfrac{dV}{dx} = \dfrac{dq}{dx} - \dfrac{ds}{dx}$. By the chain rule, the RHS equals $\dfrac{dq}{dp}\dfrac{dp}{dx} - \dfrac{ds}{dr}\dfrac{dr}{dx}$.

We now calculate these 4 terms:

$\dfrac{dp}{dx} = \cos(x), \dfrac{dq}{dp} =\dfrac{1}{p} = \dfrac{1}{\sin x}$

$\dfrac{dr}{dx} = 4x^3-3, \dfrac{ds}{dr} = 10 r^9 = 10(x^4-3x)^9$.

Substituting these in, we find that the RHS = $\dfrac{1}{\sin x} \cos(x) - 10(x^4-3x)^9(4x^3-3)$

On the other hand, if you do need to show your working to that extent, I think I should say that I find the way you write things out very confusing, with pieces of calculation appearing at semi-arbitrary places on the page with little connection between the pieces. A mathematical argument should flow from step to step - it shouldn't be necessary for me to search the page trying to work out how two pieces of calculation are connected.

If I had to give that level of working, I would probably go:

$V(x) = \ln(\sin(x)) - (x^4-3x)^{10}$. Write $p = \sin(x), q = \ln(p), r = x^4 - 3x, s = r^{10}$.

Then $V(x) = q - s$ and $\dfrac{dV}{dx} = \dfrac{dq}{dx} - \dfrac{ds}{dx}$. By the chain rule, the RHS equals $\dfrac{dq}{dp}\dfrac{dp}{dx} - \dfrac{ds}{dr}\dfrac{dr}{dx}$.

We now calculate these 4 terms:

$\dfrac{dp}{dx} = \cos(x), \dfrac{dq}{dp} =\dfrac{1}{p} = \dfrac{1}{\sin x}$

$\dfrac{dr}{dx} = 4x^3-3, \dfrac{ds}{dr} = 10 r^9 = 10(x^4-3x)^9$.

Substituting these in, we find that the RHS = $\dfrac{1}{\sin x} \cos(x) - 10(x^4-3x)^9(4x^3-3)$

Thank you for your honest opinion.

With little space given and my handwriting often a little larger, it’s hard to find room to properly organise it.

In my previous math questionnaire, I had cut out the boring parts and the tutor asked me to include the formulas and how I came to find my solution, so now I go over board for that soul purpose.

Original post by KingRich

Thank you for your honest opinion.

With little space given and my handwriting often a little larger, it’s hard to find room to properly organise it.

In my previous math questionnaire, I had cut out the boring parts and the tutor asked me to include the formulas and how I came to find my solution, so now I go over board for that soul purpose.

With little space given and my handwriting often a little larger, it’s hard to find room to properly organise it.

In my previous math questionnaire, I had cut out the boring parts and the tutor asked me to include the formulas and how I came to find my solution, so now I go over board for that soul purpose.

In simple terms, the normal flow should be as with the written word - left to right, and then onto the next line.

If you want to break that convention, you should include some level of 'signposting' (arrows or similar), but to be honest there aren't many times you should break it. [Diagrams are an obvious exception].

However you do things, you should have *some* kind of connection between each stage in the argument - typically a few words of English. (You'll note I wrote about 5 times as much English as you did in your answer).

I also think the red boxes are more of a distraction than a help (in particular, many people seem to use an "unwritten convention" that calculations "in a box" are rough workings that generally be ignored. So the boxes are actively pushing me to ignore what I guess you consider the important parts).

[Much of this is based on feedback I got myself during my first few weeks at university.]

Another minor note is that you should pretend you have infinite paper space. If you don't have enough space, simply ask for extra answer sheets rather than trying to cram everything (then correctly signpost by saying "continue on extra answer sheet page blah" as a nice gesture). As a personal note, I write stuff even larger than yours (most of my pages contain 10 lines of writing at max), and I have never gone into an exam without asking extra answer sheets.

It's not worth sacrificing clarity for the sake of saving trees.

(P.S. I googled "how many trees can you save by saving paper", and the result is kinda funny - but that's off-topic here)

It's not worth sacrificing clarity for the sake of saving trees.

(P.S. I googled "how many trees can you save by saving paper", and the result is kinda funny - but that's off-topic here)

(edited 3 months ago)

Original post by DFranklin

In simple terms, the normal flow should be as with the written word - left to right, and then onto the next line.

If you want to break that convention, you should include some level of 'signposting' (arrows or similar), but to be honest there aren't many times you should break it. [Diagrams are an obvious exception].

However you do things, you should have *some* kind of connection between each stage in the argument - typically a few words of English. (You'll note I wrote about 5 times as much English as you did in your answer).

I also think the red boxes are more of a distraction than a help (in particular, many people seem to use an "unwritten convention" that calculations "in a box" are rough workings that generally be ignored. So the boxes are actively pushing me to ignore what I guess you consider the important parts).

[Much of this is based on feedback I got myself during my first few weeks at university.]

If you want to break that convention, you should include some level of 'signposting' (arrows or similar), but to be honest there aren't many times you should break it. [Diagrams are an obvious exception].

However you do things, you should have *some* kind of connection between each stage in the argument - typically a few words of English. (You'll note I wrote about 5 times as much English as you did in your answer).

I also think the red boxes are more of a distraction than a help (in particular, many people seem to use an "unwritten convention" that calculations "in a box" are rough workings that generally be ignored. So the boxes are actively pushing me to ignore what I guess you consider the important parts).

[Much of this is based on feedback I got myself during my first few weeks at university.]

I see. So, as you wrote in your answer we now calculate these terms etc, this can be included within an answer if necessary?

The take away is to make sure it flows downwards without jumping left to right.

So, first line…..

Second line…..

no, putting information adjacent to the first line that needs to be put in the third line for example..

As long as what I write is clear, even if I use a few words, it will be accepted?

Original post by KingRich

I see. So, as you wrote in your answer we now calculate these terms etc, this can be included within an answer if necessary?

The take away is to make sure it flows downwards without jumping left to right.

So, first line…..

Second line…..

no, putting information adjacent to the first line that needs to be put in the third line for example..

As long as what I write is clear, even if I use a few words, it will be accepted?

The take away is to make sure it flows downwards without jumping left to right.

So, first line…..

Second line…..

no, putting information adjacent to the first line that needs to be put in the third line for example..

As long as what I write is clear, even if I use a few words, it will be accepted?

It should read left to right and then top to bottom (i.e. exactly the same order as when you're reading a book).

On some levels it's not a big deal - you're unlikely to lose marks at this level. It's just kind of frustrating to see someone saying "I'm doing all this to make it clear what I'm doing" but the way they're laying everything out is not at all clear.

[And let's be honest - your course is a bit bone-headed about what they expect you to do - at the end of the day you have to do what they want, even if someone like me thinks it's stupid].

Original post by tonyiptony

Another minor note is that you should pretend you have infinite paper space. If you don't have enough space, simply ask for extra answer sheets rather than trying to cram everything (then correctly signpost by saying "continue on extra answer sheet page blah" as a nice gesture). As a personal note, I write stuff even larger than yours (most of my pages contain 10 lines of writing at max), and I have never gone into an exam without asking extra answer sheets.

Original post by DFranklin

It should read left to right and then top to bottom (i.e. exactly the same order as when you're reading a book).

On some levels it's not a big deal - you're unlikely to lose marks at this level. It's just kind of frustrating to see someone saying "I'm doing all this to make it clear what I'm doing" but the way they're laying everything out is not at all clear.

[And let's be honest - your course is a bit bone-headed about what they expect you to do - at the end of the day you have to do what they want, even if someone like me thinks it's stupid].

On some levels it's not a big deal - you're unlikely to lose marks at this level. It's just kind of frustrating to see someone saying "I'm doing all this to make it clear what I'm doing" but the way they're laying everything out is not at all clear.

[And let's be honest - your course is a bit bone-headed about what they expect you to do - at the end of the day you have to do what they want, even if someone like me thinks it's stupid].

😅😅 this is true. The course is a little meh at times.

Tutors have different preferences, too.

It’s the same as when I write essays and I’m asked to use Harvard style but then one tutor asks for a specific order and then another tutor asks for a different order.

You have to fulfil the specific tutors requirements on that specific paper to get distinction, so it’s frustrating.

Reminds me of school all over again 😅

I appreciate your feedback a lot though. To me, when I read it, I think the flow seems obvious lol. Unfortunately, I have no one at home to ask.

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