Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2020 / Paper 1 / 3 / Solution

Apply the product rule to

x sin (1/ x)

and the chain rule to the sine. Since

d (1/ x) / d x = - 1/ x^{2}

, the derivative is

\frac{d y}{d x} = sin \frac{1}{x} - \frac{1}{x} cos \frac{1}{x}, x \neq = 0.

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