   Another maths thread
  Hi, another maths question from me (God, I hate this subject):Supposing you've got a function:f(x) = x/(x+1)You've got to then differentiate said function, and find the critical points.  I would be able to do this fine if it wasn't a reciprocal like that, so how do I rearrange the thing for differentiation?Or do I use something else, like the Product/Quotient Rule?I'm clueless, can't find any hint anywhere on Google, in my notes or textbook, and the lecturer is an idiot.  There's a class of 120 struggling because of how bad the teaching is.Can anybody help at all?Thanks in advance,ukdeveloper.   
Quote:Original post by ukdeveloperI would be able to do this fine if it wasn't a reciprocal like that...That's not a reciprocal, it's called a "quotient". There, now you should know what to do with it. [smile]Edit: Oh, and good luck trying to find critical points...   ;Quote:Original post by ukdeveloperHi, another maths question from me (God, I hate this subject):Supposing you've got a function:f(x) = x/(x+1)You've got to then differentiate said function, and find the critical points.  I would be able to do this fine if it wasn't a reciprocal like that, so how do I rearrange the thing for differentiation?Or do I use something else, like the Product/Quotient Rule?I'm clueless, can't find any hint anywhere on Google, in my notes or textbook, and the lecturer is an idiot.  There's a class of 120 struggling because of how bad the teaching is.Can anybody help at all?Thanks in advance,ukdeveloper.I'd prefer to write the equation like f(x) = x (x+1)-1. From there you can simply apply the product rule. I prefer the product rule because it is easier to make a silly mistake using the quotient rule, although the quotient rule is entirely appropriate in your example. The only wrinkle is that you are going to end up using the chain rule to get the derivative of (x+1)-1. However, you'll soon start seeing expressions like that and just writing down the derivative rather than think about the chain rule.Just to make sure you're on the right track:Product rule:  D[f*g] = D[f]*g + f*D[g]Quotient rule: D[f/g] = (g*D[f] - D[g]*f)/g2(here D[f] means you're taking the derivative of some function f);Quote:Original post by ukdeveloperHi, another maths question from me (God, I hate this subject):Supposing you've got a function:f(x) = x/(x+1)You've got to then differentiate said function, and find the critical points.  I would be able to do this fine if it wasn't a reciprocal like that, so how do I rearrange the thing for differentiation?Or do I use something else, like the Product/Quotient Rule?I'm clueless, can't find any hint anywhere on Google, in my notes or textbook, and the lecturer is an idiot.  There's a class of 120 struggling because of how bad the teaching is.Can anybody help at all?Thanks in advance,ukdeveloper.Differentiating is matter of applying few simple rules (that can be trivially derived if forgotten). This is done with "quotient rule" (search google). (You might be confused by rule formula using "f" for function, it has nothing to do with your f)We have:f(x)=x/(x+1)applying quotient rule (can be remembered as "bottom times derivative of top minus top times derivative of bottom divided by bottom squared")we get:f'(x)=(edit: solution is hiddeh, if you want quote the post and see.)BTW, as nice lil project you can write differenciator program using the rules :-)   ;Quote:Original post by Dmytryapplying quotient rule (can be remembered as "bottom times derivative of top minus top times derivative of bottom divided by bottom squared")A neat little rhyming jingle I learned to remember it is:"Low d-high minus high d-low over low squared"   ;  I found it better for me to remember how equation looks, for longer equations. Never undestood why some (or most) people use song/text/whatever mnemonics, actually... for short equations it could be possible to remember that "quotient rule means [that]" in a way how one remembers that, for example, what does "horse" mean (without using mnemonics to remember that it is mammal with bilateral symmetry, four legs, one head, one tail, and so on).[Edited by - Dmytry on December 6, 2005 9:17:43 AM];  I'd use my TI-89.   ;  Quotient rule is generally easy to remember, but if ever I get stuck:"vdu minus udv all over v squared"vdu = Visual Display Unit   ;  Eh, you can easily derive the quotient rule from the definition of the derivative, should you ever get stuck. Or from the product rule, as jjd suggested.   ;  I use the quotient rule song:lowwwww-deeee-hiiiiii minus hiiii-deeee-lowwwww allova lowwwww-squareddddd.x/(x+1)((x+1)*1 - x)/(x+1)^21/(x+1)^2so you can't have x = -1For derivatives, I like to user Calc 101, a website that can simplify derivatives for you (for free, and with steps!).Best of luck.[Edited by - Vasant56 on December 7, 2005 7:36:12 AM]