| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2010 |
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| Session | June |
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| Topic | Implicit equations and differentiation |
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1 The variables \(x\) and \(y\) are such that \(y = - 1\) when \(x = 1\) and
$$x ^ { 2 } + y ^ { 2 } + \left( \frac { \mathrm { d } y } { \mathrm {~d} x } \right) ^ { 3 } = 29$$
Find the values of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) when \(x = 1\).