 Solution

ID: 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/solution

Differentiate the product

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

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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