Question

cosx的y次方等于siny的x次方,求导数.要详细过程.谢谢

Answer 1

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)