Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Discrete mathematics, probability and continuous mathematics / 5 / a / i

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- Solution i

Solution

Differentiate the product

4 (x - 1)^{- 2} (x + 1)^{- 1}

using the product rule and chain rule:

f^{'} (x) = - 8 (x - 1)^{- 3} (x + 1)^{- 1} - 4 (x - 1)^{- 2} (x + 1)^{- 2} .

Combining terms over a common denominator gives

f^{'} (x) = - \frac{4 ( 3 x + 1 )}{( x - 1 ) ^{3} ( x + 1 ) ^{2}}, x \neq = \pm 1.

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