1. The problem statement, all variables and given/known data Having started to differentiate Ln(cos(5x)) wrt x I checked the answer with WolframAlpha & got a different method & answer too. 2. Relevant equations differentiate ln(cos(5x)) 3. The attempt at a solution I used the Chain rule d(ln(cos(5x)))/dx = d(ln(u))/du * du/dx Where u = cos(5x) d(ln(u))/du = 1/u which I have in a table of standard derivatives = 1/(cos(5x) du/dx = -sin(5x) again, from a table of standard derivatives. So according to me d(ln(cos(5x)))/dx = 1/cos(5x) * -sin(5x) WolframAlpha goes a different route & has the answer -5 tan(5x) I see how this differs from mine so; 1. why am I wrong, 2. how did WA get from sec(5x)(sin(5x)(-(d(5x)/dx))) to -5tan(5x). i.e how is tan defined in terms of sec? Sorry to be dense!