Question

Find dy./dx if x² +y2 =4xy
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Answer 1

To find dy/dx for the equation x² + y² = 4xy, one must use implicit differentiation and then isolate dy/dx to solve for it. The result is dy/dx = (4y - 2x) / (2y - 4x).

Step-by-step explanation:

The student asked to find dy/dx for the equation x² + y² = 4xy. To solve this, we need to use implicit differentiation because y is not expressed explicitly as a function of x. Differentiating both sides of the equation with respect to x gives us:

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• 2x + 2y(dy/dx) = 4x(dy/dx) + 4y
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• Now, we rearrange the terms to isolate dy/dx on one side:
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• 2y(dy/dx) - 4x(dy/dx) = 4y - 2x
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• (2y - 4x)(dy/dx) = 4y - 2x
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• Divide both sides by (2y - 4x) to solve for dy/dx:
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• dy/dx = (4y - 2x) / (2y - 4x)

This gives us the derivative of y with respect to x for the given equation.