已知xy-sin(πy^2)=0 x^2y+siny^2=0求y的一阶导数
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![已知xy-sin(πy^2)=0 x^2y+siny^2=0求y的一阶导数](/uploads/image/z/10265811-51-1.jpg?t=%E5%B7%B2%E7%9F%A5xy-sin%28%CF%80y%5E2%29%3D0+x%5E2y%2Bsiny%5E2%3D0%E6%B1%82y%E7%9A%84%E4%B8%80%E9%98%B6%E5%AF%BC%E6%95%B0)
已知xy-sin(πy^2)=0 x^2y+siny^2=0求y的一阶导数
已知xy-sin(πy^2)=0 x^2y+siny^2=0求y的一阶导数
已知xy-sin(πy^2)=0 x^2y+siny^2=0求y的一阶导数
两边对x求导:y+xy'-cos(πy2) (2πyy')=0 y'[x-2πycos(πy^2)]=-y
y' = 2πcos(πy^2) - x/y (1)
2xy+x^2 y'+ 2yy'cos(y^2)=0 y'[x^2+2ycos(y^2)]=-2xy
y' = -2xy / [x^2+2ycos(y^2)] (2)