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Princeton Review Help page 125

Posted: Wed Aug 05, 2009 1:33 pm
by toughluck
For the second example that it gives for the chain rule with z=F(u,v,y) where u=f(v,x) & v=g(x,y) I don't really understand the diagram that is drawn & when I got a different answer then the one given by the book for the derivative of z with respect to y.

Since it tells you to think of each arrow meaning depends on I only drew an arrow if the function used one of those variables so I had the following

z with arrows to u,v and y
u with arrows to v and x
v with arrows to x and y

and came up with the following

dz/dy=dz/dy+dz/dv dv/dy+ dz/du du/dv dv/dy

could someone explain to me where i went wrong because I feel like at the very least the diagram has to be wrong because it gives five paths to y and only three are used.

Re: Princeton Review Help page 125

Posted: Thu Aug 06, 2009 1:03 am
by lime
Check the "typos" question in the FAQ.

Re: Princeton Review Help page 125

Posted: Thu Aug 06, 2009 9:26 am
by toughluck
Well like I said I knew that the diagram at the very least had to be wrong but I don't see how the diagram given in the FAQ would make any sense either unless there was another typo on the same page and the problem was suposed to be: z=F(u,v,y) where v=f(u,x) and u=g(x,y) because how could you take a partial of u with respect to y if u were written in terms of v and x like the problem states that it is.