IBSQUARED Posted November 23, 2008 Report Share Posted November 23, 2008 Could someone please go over differentiating y = ln (5x) using first principles The answer should come out to 1/x Thanks Reply Link to post Share on other sites More sharing options...
moneyfaery Posted November 24, 2008 Report Share Posted November 24, 2008 Do you mean 5/x? The derivative of lnx is 1/x Reply Link to post Share on other sites More sharing options...
Hedron123 Posted November 24, 2008 Report Share Posted November 24, 2008 As moneyfaery said: the derivative of ln x is equal to 1/x. The derivative of ln (5x) is = 1 /5x times 5 (derivative of 5x). So: the answer is 1 / x Reply Link to post Share on other sites More sharing options...
moneyfaery Posted November 24, 2008 Report Share Posted November 24, 2008 Is it? Oops, can't remember. It's been a year. Reply Link to post Share on other sites More sharing options...
IBSQUARED Posted November 24, 2008 Author Report Share Posted November 24, 2008 Yeah i know the ln rule.. but a question in our text asked to prove its 1/x using first principles so the f(x+h) - f(x) -------------- h Reply Link to post Share on other sites More sharing options...
Abu Posted November 24, 2008 Report Share Posted November 24, 2008 IBSQUARED - We don't do first principles for Maths HL Reply Link to post Share on other sites More sharing options...
ezex Posted November 25, 2008 Report Share Posted November 25, 2008 Cmon...give the poor kid a hand! Here goes, try to keep up: deriv of ln(x) = lim(h->0) [ ln(x+h) - ln(x) ] / h from the definition of the deriv. = lim ln((x+h)/x) / h from log rules when subtracting two logs = lim (1/h) ln(1 + h/x) just took the 1/h outside = lim [ ln (1 + h/x)^(1/h) ]. rules of logs when you convert the coeficient to exponent Set u=h/x and substitute (so things fit , mathematicians get to do that): lim(u->0) [ ln (1 + u)^(1/(ux)) ] replaced formula = 1/x ln [ lim(u->0) (1 + u)^(1/u) ] brought down a 1/x from the exponent using rules of logs again = 1/x ln (e) replaced that whole mess after ln by e because lim(u->0) (1 + u)^(1/u) is the formal definition of e, look it up = 1/x. uh...ya, if you don't know what i did to get to this step you probably didn't follow on the proof so i'm not gonna say that ln (e) = 1...dammit Reply Link to post Share on other sites More sharing options...
Abu Posted November 25, 2008 Report Share Posted November 25, 2008 Not all of us are math prodigies! Reply Link to post Share on other sites More sharing options...
ezex Posted November 25, 2008 Report Share Posted November 25, 2008 pfft this was math was baby...lol Reply Link to post Share on other sites More sharing options...
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