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...Compute partial derivatives with chain rule formulae these are the most frequently used ones if w f x y and t such that all dierentiable then dw wdx wdy dt for each i n m example given ln u v z cos sin nd both by using expressing explicitly as a function of before dierentiating solution first we apply wdu wdv wdz costsint sintcost next express substituting into to get cost therefore yz zx xy s this is derivative problem so st p write formulas giving dependent variable respect independent xyz functions an implicit dierentiation must be just view everywhere occurs when dierentiate sides equation step solve in resulting above do same xz zy surface plane tangent at point vector will normal from have hence or one can also set case fx fy fz suppose show notice rcos rsin r rst order...