Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 1 / 18 / d

View $a=a(b,c)$ with $b=b(d,e)$ and $c=c(d,e)$. Hold $e$ fixed and apply the multivariable chain rule:Dividing the changes along the fixed-$e$ variation by $dd$ gives exactly the two terms in the question. Thus the simpler expression isThe subscripts specify which coordinate is held fixed and must be retained.