怎么对x求导啊？急～～～

Question

如题所述

Answer 1

√(x^2+y^2) = e^(arctan(y/x))
x^2 +y^2 =e^(2arctan(y/x))
2x + 2yy' = [2/( 1+ (y/x)^2 )] [ -y/x^2 + (1/x)y' ] e^(2arctan(y/x))
x+yy' = [1/(x^2+y^2)] [ -y + xy' ] e^(2arctan(y/x))
= [1/(x^2+y^2)] [ -y + xy' ] (x^2+y^2)
= -y + xy'
(y-x)y' = -(x+y)
y' = (x+y)/(x-y)
= 1 + 2y/(x-y)
y'' = 2[ (x-y)y' - y(1-y') ] /(x-y)^2
= 2( xy' - y) /(x-y)^2
= 2[ x(x+y)/(x-y) -y ] /(x-y)^2
= 2[ x(x+y) -y(x-y) ] /(x-y)^3
=2(x^2+y^2)/(x-y)^3