| Exam Board | OCR MEI |
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| Module | C3 (Core Mathematics 3) |
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| Topic | Implicit equations and differentiation |
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1 A curve has implicit equation \(y ^ { 2 } + 2 x \ln y = x ^ { 2 }\).
Verify that the point \(( 1,1 )\) lies on the curve, and find the gradient of the curve at this point.