cosx的y次方等于siny的x次方,求导数.要详细过程.谢谢

要使等式有意义,则cosx>0,siny>0
等式两边取自然对数有ylncosx=xlnsiny
等式两边对x求导有
d(ylncosx)/dx=d(xlnsiny)/dx
[dy*lncosx+y*(1/cosx)*(-sinx)*dx]/dx=[dx*lnsiny+x*(1/siny)*cosy*dy]/dx
lncosx*dy/dx+(-ytanx)=lnsiny+xcoty*dy/dx
dy/dx=(lnsiny+ytanx)/(lncosx-xcoty)