Differential Problem

hlbeckley · July 6th, 2009, 1:16 pm

Hi all, please help me.I have the question:f(x,y) = x^2 + y^2, where x=sin2theta and y=cos2thetaWhat is df/dtheta?I just dont know where to begin pls can some one give guidance to me? I want to try understand the porblem, not simply just get an answerthanks

ACD · July 6th, 2009, 1:32 pm

Look up the chain rule

daveangel · July 6th, 2009, 1:33 pm

are you kidding ?

hlbeckley · July 6th, 2009, 1:34 pm

I kid you not!

daveangel · July 6th, 2009, 1:44 pm

hint: for any x

hlbeckley · July 6th, 2009, 1:56 pm

Ok sure get that for A-Level dayshere's my mind thinking...pls hold the laughterx = sin2theta thus x^2 = sin^2.2thetay = cos2theta thus y^2 = cos^2.2thetaso from Q; f(x,y) = x^2 + y^2f(x,y) = sin^2.2theta + cos^2.2thetaf(x,y) = 2theta(sin^2+cos^2) = 2theta(1)df/dtheta is = 2???

hlbeckley · July 6th, 2009, 2:09 pm

hang on my factorising is offsin^2.2theta + cos^2.2theta = 1so f(x,y) now = 1and the f' of 1 = 0

batesh · July 9th, 2009, 7:35 am

Without using the trig identity you can go down the total derivative route to arrive at the same answer.