对于x=cos(y/x),求dy/dx.

来源:学生作业帮助网 编辑:作业帮 时间:2024/07/13 03:35:43
对于x=cos(y/x),求dy/dx.
x){~]}:66TT$/!QVXV83,QQ[_g|m=Ov,yz= YO+*ՇG*ЯЭ@xԱJ[ iNJ @p

对于x=cos(y/x),求dy/dx.
对于x=cos(y/x),求dy/dx.

对于x=cos(y/x),求dy/dx.
∵x=cos(y/x)
==>1=-sin(y/x)*(xy'-y)/x^2 (等式两端对x求导)
==>xy'-y=-x^2/sin(y/x)
==>xy'=y-x^2/sin(y/x)
==>y'=y/x-x/sin(y/x)
∴dy/dx=y'=y/x-x/sin(y/x).