隐函数求导(要过程)
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解:等式两边均对x求导
(注(arctanx)'= 1/(1+x^2)), ((ln√(x^2+y^2))'=√(x^2+y^2)*(x+yy') /√(x^2+y^2)*
=(x+yy')/(x^2+y^2)
1/[(1+(y/x)^2]*(y'x-y)/x^2=(x+yy')/(x^2+y^2)
即 x^2/(x^2+y^2)*(y'x-y)/x^2==(x+yy')/(x^2+y^2)
y'x-y=x+yy'
y'=(x+y)/(x-y)
(注(arctanx)'= 1/(1+x^2)), ((ln√(x^2+y^2))'=√(x^2+y^2)*(x+yy') /√(x^2+y^2)*
=(x+yy')/(x^2+y^2)
1/[(1+(y/x)^2]*(y'x-y)/x^2=(x+yy')/(x^2+y^2)
即 x^2/(x^2+y^2)*(y'x-y)/x^2==(x+yy')/(x^2+y^2)
y'x-y=x+yy'
y'=(x+y)/(x-y)
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