I'm having such a hard time with this one :/
A model for the surface area of a human body is given by , where w is the weight (in pounds), h is the height (in inches), and S is measured in square feet. If the errors in measurement of w and h are at most 2%, use differentials to estimate the maximum percentage error in the calculated surface area.
The book's answer is 2.3%
i know this is old, but i had that problem in my calculus homework today and i'm sure other people will in the future.
i didn't use lns or anything -
if you just try to find dS/S, it works out.
for ds, you need dS/dw + dS/dh
you end up with dS/S = ((.425)(.1091)(w^(.425-1))(h^7.25)dw + (.725)(.1091)(w^.425)(h^(.725-1))dh) / ((.1091)(w^.425)(h^.725))
do some cancellation and you get dS/S = .425dw/w + .725dh/h and then plug in .02 for (dw/w) and (dh/h)
it's essentially the same thing i guess, but i understand it better that way.