show me how to solve this problem: (xy)^2=2x+9y^2 implicit diff...

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Differentiate (xy)2=2x+9y2 implicitly with respect to x:

x2y2=2x+9y2,

2xy2+2x2ydy/dx=2+18ydy/dx from which:

(2x2y-18y)dy/dx=2-2xy2; (x2y-9y)dy/dx=1-xy2;

dy/dx=(1-xy2)/(x2y-9y), which can also be written dy/dx=(xy2-1)/(9y-x2y).

ago by Top Rated User (1.2m points)

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