Given the relation: x^4 + 2x^2y^2 + y^4 = 4y^2, attempt to find dy/dx at each of

Question

Given the relation: x^4 + 2x^2y^2 + y^4 = 4y^2, attempt to find dy/dx at each of the
following points. If it is impossible to find dy/dx ,give a reason why this is so. Hint: Sketch the given relation first. (a) (1,2),   (b) (-1,1),    (c) (0,0),      (d) (0,-2). Given the relation: x^4 + 2x^2y^2 + y^4 = 4y^2, attempt to find dy/dx at each of the
following points. If it is impossible to find dy/dx ,give a reason why this is so. Hint: Sketch the given relation first. (a) (1,2),   (b) (-1,1),    (c) (0,0),      (d) (0,-2).

Explanation / Answer

dy/dx of the relation is equal to 4x^3 +(4y^2)x. Remember, since the derivative is with respect to x, the y components are treated as constants, thereby dropping y^4 and 4y^2 to 0. Evaluating the new relation at the given points amounts to substitution for x and y.

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