| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2007 |
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| Session | November |
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| Topic | Implicit equations and differentiation |
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5 The positive variables \(x\) and \(y\) are related by
$$y = x ^ { 2 } + 2 \ln ( x y )$$
Find the values of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) when both \(x\) and \(y\) are equal to 1 .