求隱函數的導數sin(x+2y)=ln xy答案要詳細的,謝了

求隱函數的導數sin(x+2y)=ln xy答案要詳細的,謝了

兩邊對x求導得:
cos(x+2y)*(1+2y')=1/(xy)*(y+xy')
xycos(x+2y)+2xyy'cos(x+2y)=y+xy'
得:y'=[y-xycos(x+2y)]/[2xycos(x+2y)-x]