Calculus Queries (1 Viewer)

[Finx]

I'm just wondering how I should set out working for a question that asks dy/dx. I use the easy method (dunno what it's called).

eg. Find dy/dx for: 2x^3 + x^2 + 3x + 8

f'(x) = 6x^2 + 2x + 3


Do I have to state that I'm using this method or anything else before I answer f'(x)?

Ta =]

 

[kaz1]

You don't have to unless the question asks you to do first principles.

 

[Finx]

So would solving dy/dx be a one-line answer?

 

[Slidey]

First principles is silly because it's not even rigourous or anything.

 

[midifile]

yes. when you are doing basic calculus you can do it iin one line

 

[kaz1]

So would solving dy/dx be a one-line answer?

Yes.

 

[Finx]

Schweet, thanks peoples =]

 

[bored of sc]

I'm just wondering how I should set out working for a question that asks dy/dx. I use the easy method (dunno what it's called).

eg. Find dy/dx for: 2x^3 + x^2 + 3x + 8

f'(x) = 6x^2 + 2x + 3


Do I have to state that I'm using this method or anything else before I answer f'(x)?

Ta =]

It's called the short method and you prove it using first principles (the 'harder'/'longer' way). What you have is perfectly fine.

Be sure you know how to do it the 'long' way as it has been tested upon in the extension 1 maths HSC exam before.

 

[The Kaiser]

I'm just wondering how I should set out working for a question that asks dy/dx. I use the easy method (dunno what it's called).

eg. Find dy/dx for: 2x^3 + x^2 + 3x + 8

f'(x) = 6x^2 + 2x + 3


Do I have to state that I'm using this method or anything else before I answer f'(x)?

Ta =]

If you want to get technical, then that is wrong because you can't say f'(x) = dy/dx even though they represent the same thing (according to my teacher, whom deducted half a mark because I did the same thing)

If you want to be safe then set your working out as follows.

y = 2x^3 + x^2 + 3x + 8

Therefore dy/dx = 6x^2 + 2x + 3

 

[lyounamu]

If you want to get technical, then that is wrong because you can't say f'(x) = dy/dx even though they represent the same thing (according to my teacher, whom deducted half a mark because I did the same thing)

If you want to be safe then set your working out as follows.

y = 2x^3 + x^2 + 3x + 8

Therefore dy/dx = 6x^2 + 2x + 3

Yeah, true. If you want to write it as f'(x), you will have to say

"Let f(x) = 2x^3 + x^2 + 3x + 8" beforehand. But I doubt you will lose mark from not doing so.

 

[tommykins]

Can someone refrsh my memory, first principles is [f(x) - f(x+h)]/h ?

 

[lyounamu]

Can someone refrsh my memory, first principles is [f(x) - f(x+h)]/h ?

Otherway around: lim h->0 (f(x+h) - f(x))/h

 

[The Kaiser]

Can someone refrsh my memory, first principles is [f(x) - f(x+h)]/h ?

{f(x+h) - f(x)}/h as h ® 0 (the limit of h)


Edit: Beaten!

 

[the-derivative]

You will rarely ever be asked to use first principles though. For differentiation... you would mainly need to remember the basic rule (don't know what it's called officially), the product, chain and quotient rule and how to differentiate logs and exponentials. Pretty easy.

 

[Aerath]

You will rarely ever be asked to use first principles though.

We got a question like that in our half yearly....and I swear I saw a couple from past HSC papers (although, it might've been other schools' papers.

 

[the-derivative]

We got a question like that in our half yearly....and I swear I saw a couple from past HSC papers (although, it might've been other schools' papers.

Really? I havent seen a first principles question in all the past HSC papers I've done - but then again I've only done papers from a few schools. I have seen it in a few prelim papers though.

 

[Aplus]

We got a question like that in our half yearly....and I swear I saw a couple from past HSC papers (although, it might've been other schools' papers.

First principles should be avoided unless forced imo. Time consuming.

 

[lsam]

Really? I havent seen a first principles question in all the past HSC papers I've done - but then again I've only done papers from a few schools. I have seen it in a few prelim papers though.

I have seen once in MX1 HSC paper.

I have seen tonnes in random school trials.

 

[Aplus]

I think they only started asking first principle questions since arecently. Apparently it had been removed from the syllabus for so many years, and when it was asked a few years ago, a lot of teachers complained or something. Anyway, since then it's been known to pop up regularly, I think.

 

[Aerath]

First principles should be avoided unless forced imo. Time consuming.

But it was like basic first principles. Like differentiating x^2 - 2x from first principles. It wasn't something like...... differentiating x^-0.5.