這是一個(gè)微分方程,按理說(shuō)應(yīng)該是求f(x)的表達(dá)式.你說(shuō)的兩邊對(duì)x求導(dǎo)是要做什么呢?
如果是求f(x)的表達(dá)式的話,
if 你的題目是dy/dx=1/1-cosy
dy/dx=1/1-cosy =>dy/dx=1-cosy=>dy/(1-cosy) =dx => dy/2sin^2(y/2)=dx => d(y/2)/sin^2(y/2)=dx =>-[d(y/2)/sin^2(y/2)]=d(-x) =>d(ctg(y/2))=d(-x) => ctg(y/2)=-x
if 你的題目是dy/dx=1/(1-cosy) (考慮到很少有人把1寫(xiě)成1/1,所以我認(rèn)為你的題目很有可能是 "dy/dx=1/(1-cosy)" )
dy/dx=1/(1-cosy) => dy-(dy)(cosy)=dx =>dy-d(siny)=dx => y-siny=x