 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2/12/a/solution

For

r > 0

, differentiate

r = x^{2} + y^{2}

while keeping the other coordinate fixed in the Cartesian coordinate system:

r_{x} = \frac{x}{r} = cos ϕ, r_{y} = \frac{y}{r} = sin ϕ .

The origin is excluded from this polar coordinates chart.

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