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...Mit opencourseware http ocw edu multivariable calculus fall for information about citing these materials or our terms of use visit source url courses mathematics lecture notes saylor www org ma attributed to page thu oct solutions ps practice exams a and b handouts non independent variables often w e have deal with g f p v t where pv nrt question if x y z c then can think what are example yz at take dierential xdx dy dz i dx constraint so taking th coecients equivalently is held constant we substitute get in general xed on be dangerous warning notati change u but this because means keeping while wh ere s ambiguity must precise deriv en wenowhave above computed when there no risk confusion keep the old notation by default area triangle sides making an angle ab sin suppose it right hypothenuse cos ways which rate r makes sense view usual changes stops being happens answers does satisfy ho compute substitution sec tan easiest here not always possible solve tials da d db total dieren plugg...