UK_Pablo 112 Report post Posted October 19, 2006 Hi all, I was searching for some info on the chain rule and came across an old post asking how to differentiate the following formula x^2 + y^2 = 4 Now not quite sure what they were on about, but i did it this way. Just want to know if i worked it out right. x^2 + y^2 -4 = 0 sqrt(4-x^2) = y so sub (4-x^2) with a letter, say u sqrt(u) = y : y' = 1/2u^-1/2 u' = 4-x^2 : 2x put it all back together and i got y' = 1/2(sqrt(4-x^2)^-1/2) * 2x which is the same as y' = x*sqrt(4-x^2)^-1/2 Was I any where near right? Thanks in advance. 0 Share this post Link to post Share on other sites
Mashiniblik 122 Report post Posted October 19, 2006 You got: y' = x*sqrt(4-x^2)^-1/2u' should be negative 2x right? and the ^-1/2 stands for sqrt(), so you should havey' = -x/sqrt(4-x^2)by my calculations.I'm guessing you had x*(4-x^2)^-1/2 and you thought "beauty, 1/2 means sqrt()", and put your sqrt() in, forgetting to change the ^-1/2 to ^-1, which puts it on the denominator. 0 Share this post Link to post Share on other sites
grhodes_at_work 1385 Report post Posted October 19, 2006 Be careful folks. This looks like schoolwork. Answer the question about whether the solution is basically correct, but do not provide detailed corrections! Remember, this forum is for game development math, not school!Forum FAQ 0 Share this post Link to post Share on other sites
alvaro 21272 Report post Posted October 19, 2006 Quote:Original post by UK_PabloHi all,I was searching for some info on the chain rule and came across an old post asking how to differentiate the following formula x^2 + y^2 = 4What does it mean to differentiate a formula? 0 Share this post Link to post Share on other sites
Paradigm Shifter 5832 Report post Posted October 19, 2006 Quote:Original post by alvaroQuote:Original post by UK_PabloHi all,I was searching for some info on the chain rule and came across an old post asking how to differentiate the following formula x^2 + y^2 = 4What does it mean to differentiate a formula?Not much, without saying which variable you are differentiating with respect to.If you differentiate that formula with respect to z, or penguin, you get 0. 0 Share this post Link to post Share on other sites
erissian 727 Report post Posted October 19, 2006 Well, in the most basic way, you can derive a formula without accounting for a particular variable.for instance:x = 5y + 2z^{2} + 5dx = 5dy + 4zdzis still a useful form. 0 Share this post Link to post Share on other sites
TheAdmiral 1122 Report post Posted October 19, 2006 That's not the tidiest way to calculate dy/dx. Note that the square-root function is not invertible (so you will have two solutions) and you have to perform a case-analysis on the sign of (4 - x²) if you're worried about getting complex solutions.Implicit formulas don't, in general, give unique explicit expressions for derivatives. If the results are satisfactory, I highly recommend you look to implicit differentiation for a single-valued answer.RegardsAdmiral 0 Share this post Link to post Share on other sites
Mashiniblik 122 Report post Posted October 20, 2006 Quote:Original post by grhodes_at_workBe careful folks. This looks like schoolwork. Answer the question about whether the solution is basically correct, but do not provide detailed corrections! Remember, this forum is for game development math, not school!sorry mate 0 Share this post Link to post Share on other sites