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Year 1 of the computer science course of the University of Oxford

Past exam of the year 1 of the computer science course of the University of Oxford

2018

Discrete mathematics, continuous mathematics, and probability

Repeated use of the <product rule> and <chain rule> gives
$$
\boxed{f'(x)=\frac{-2x}{(1+x^2)^2},\quad f''(x)=\frac{2(3x^2-1)}{(1+x^2)^3},\quad f'''(x)=\frac{24x(1-x^2)}{(1+x^2)^4}.}
$$
The denominators are strictly positive on the whole real line, making the signs in the next parts easy to read.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 6 / a / Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 6 / a / Solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 6 / a / Solution

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