求隐导 arctan y⼀x=ln根号下x方+y方

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2024-11-24 00:19:07
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回答1:

两边对x求导

1/[1+(y/x)^2]×(y/x)'=1/2×1/(x^2+y^2)×(x^2+y^2)',也就是:

x^2/(x^2+y^2)×(xy'-y)/x^2=1/2×1/(x^2+y^2)×(2x+2yy')

化简得:y'=(2x+y)/(x-2y)