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Implicit differentiation - please see http://archives.math.utk.edu/visual.calculus/3/implicit.4/index.html - for the solution of the second problem I don't understand how to get from the second step to the third. What happened to the cos(x/y) and y^2 ?
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divide the equation in the second step by cos(x/y)
there your assuming cos(x/y) is not equal to zero and y^2 is not infinite. so other term should be equal zero
not really assuming... if sin(x/y) =1/2 cos(x/y) != 0
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