 Solution

ID: 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/solution

View

a = a (b, c)

with

b = b (d, e)

and

c = c (d, e)

. Hold

e

d a = (\frac{\partial a}{\partial b})_{c} d b + (\frac{\partial a}{\partial c})_{b} d c .

Dividing the changes along the fixed-

e

dd

gives exactly the two terms in the question. Thus the simpler expression is

(\frac{\partial a}{\partial d})_{e} .

The subscripts specify which coordinate is held fixed and must be retained.

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