Final answer:
To solve for dy/dx at the point (1,1) for the equation x + 2xy - y² = 2, implicit differentiation must be used. However, the differentiation leads to an inconsistency, suggesting an error in the process or in the provided equation. A reassessment is required to give an accurate answer.
Step-by-step explanation:
The student is asking to find the derivative dy/dx at the point (1,1) for the given implicit function x + 2xy - y² = 2. To find this, we need to use the implicit differentiation technique. Differentiating both sides of the equation with respect to x, we get:
1 + 2(y + x(dy/dx)) - 2y(dy/dx) = 0
When we substitute (1,1) into the differentiated equation, we have:
1 + 2(1 + (dy/dx)) - 2(1)(dy/dx) = 0
Solve for (dy/dx) when x = 1 and y = 1:
1 + 2 + 2(dy/dx) - 2(dy/dx) = 0 ⇒ 3 = 0, which does not make sense for a derivative. It seems there is an error in the differentiation process or the function provided. Therefore, reconsidering the original function or the differentiation steps is necessary to give a correct answer.