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方程arctan(y/x)=ln√(x²+y²)两边对x求导
人气:102 ℃ 时间:2020-01-28 14:05:11
解答
arctan(y/x)=1/2*ln(x^2+y^2)两边对x求导:1/(1+y^2/x^2)* (y/x)'=1/2*1/(x^2+y^2)*(x^2+y^2)'x^2/(x^2+y^2)* (xy'-y)/x^2=1/(x^2+y^2)*(x+yy')xy'-y=x+yy'y'=(x+y)/(x-y)
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