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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: NE2000 on January 01, 2009, 05:35:30 pm

Title: Working out for differentiation
Post by: NE2000 on January 01, 2009, 05:35:30 pm: I was going through differentiation for methods. I have MathsQuest and as usual the working out they show in examples is too excessive at times for me to follow it...but now I've started to do chain rule, product rule and quotient rule without any working out...just write down the answer. Is that fine for these parts of methods or should we be, for example with the product rule, be defining u(x), v(x), u'(x) and v'(x)?

The same applies to deriving logarithmic, exponentials and trig. MathsQuest examples have working out but I'm pretty much just going straight to the answer.
Title: Re: Working out for differentiation
Post by: Mao on January 01, 2009, 05:46:47 pm: not necessarily defining, but normally you should write down the rule.
It all depends on how many marks a question is.
Title: Re: Working out for differentiation
Post by: dekoyl on January 01, 2009, 05:48:17 pm: You'll encounter those questions on exams which is worth usually 2 marks (actually I'm not too sure. The example below might be worth only 1 mark). I don't write out "using the product rule" but you have to show the examiner that you used the product rule or quotient rule.

So, for example:
$log_e(2x) = \frac1{2x}(2)$

$=\frac1{x}$

That's what I'd do anyway :P

Edit: I didn't write out the quotient/product rules because I was less comfortable with using the formula as textbooks give it. What I remembered was "keep first, deriv second plus keep second, deriv first" for product and "keep bot, deriv top minus keep top, deriv bot" for quotient and just chanted it in my head when I did it.

Edit 2: However if a question was worth 3 marks, I'd do the formula like what Mao said below.
Title: Re: Working out for differentiation
Post by: Mao on January 01, 2009, 05:51:02 pm: Quote from: dekoyl on January 01, 2009, 05:48:17 pm
You'll encounter those questions on exams which is worth usually 2 marks. I don't write out "using the product rule" but you have to show the examiner that you used the product rule or quotient rule.

So, for example:
$log_e(2x) = \frac1{2x}(2)$

$=\frac1{x}$

That's what I'd do anyway :P

its useful to just write down $\frac{d}{dx}(f\circ g) = \frac{df}{dg}\cdot \frac{dg}{dx}$ , $\frac{d}{dx}(f\times g)=\frac{df}{dx}\times g(x)+\frac{dg}{dx}\times f(x)$ and the quotient rule which i cbf typing to indicate what you are doing
Title: Re: Working out for differentiation
Post by: NE2000 on January 02, 2009, 08:57:15 am: Ok so just write the product and quotient rules to be safe. What about the chain rule?
Title: Re: Working out for differentiation
Post by: NE2000 on January 02, 2009, 03:09:41 pm: Also, when determining the nature of a stationary point, is the gradient table (with just + and - signs) fine for working out? So we don't really need to work out the value of the derivative function either side of the x-intercept but rather just whether it is > 0 or < 0

Secondly, do you think if I went through a question referring to stationary points as S.P. and then at the end said the stationary point is...then would the examiners know what I'm talking about? The same applies to abbreviations like x-int and y-int where the examiners will know what you're talking about but just want to make sure they aren't really strict on that stuff.
Title: Re: Working out for differentiation
Post by: Mao on January 04, 2009, 04:52:44 pm: the gradient table is fine, though I would still recommend you to work out the value of the derivative. It may be a little hard to explain if you popped out some >0 or <0 with no reasoning.

and they would know acronyms/abbreviations. However, don't really expect many 'explain' type of questions in the exam.
Title: Re: Working out for differentiation
Post by: NE2000 on January 04, 2009, 08:29:16 pm: Not so much 'explain type' but I just thought you were meant to show the examiner how you were going to work it out.

Eg:
"for stationary points, let dy/dx = 0"
Work it out
"(x,y) is a stationary point"
Title: Re: Working out for differentiation
Post by: methodsboy on January 04, 2009, 09:11:45 pm: Quote from: NE2000 on January 01, 2009, 05:35:30 pm
I was going through differentiation for methods. I have MathsQuest and as usual the working out they show in examples is too excessive at times for me to follow it...but now I've started to do chain rule, product rule and quotient rule without any working out...just write down the answer. Is that fine for these parts of methods or should we be, for example with the product rule, be defining u(x), v(x), u'(x) and v'(x)?

The same applies to deriving logarithmic, exponentials and trig. MathsQuest examples have working out but I'm pretty much just going straight to the answer.
You dont necessarily need to define everything. Make sure you state "Chain Rule" or write down the formala for it (this applies to general equations such as x^2+3x blah.blah. Then do your working out.
When you diff. logs, exponentials and trig, just write dy/dx etc.
Hope that helps :)
Title: Re: Working out for differentiation
Post by: pHysiX on January 20, 2009, 06:15:52 pm: hmm you don't have to write the rule, just state wat u will be using to be safe. that's wat i did =]