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If x 2xy−y²=2, then at the point (1,1), dy/dx is?

User Ananda
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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.

User Ngokevin
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