 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/1/a/solution

Write the rational expression as

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

and apply the chain rule:

\frac{d}{d x} \frac{1}{x ^{2} + 4} = - \frac{2 x}{( x ^{2} + 4 ) ^{2}} .

The denominator is positive for every real

x

, so the derivative is defined throughout the real line.

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