 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/4/solution

d x / d t = e^{t} \neq = 0

and

d y / d t = cos t

. Therefore

d y / d x = e^{- t} cos t

. The condition

x = e^{t} = 1

gives

t = 0

, so

\frac{d y}{d x}_{x = 1} = 1.

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