设siny+e的x次方-xy²=0,求dy/dx

问题描述:

设siny+e的x次方-xy²=0,求dy/dx

siny+e的x次方-xy²=0
y'cosy+e^x-y^2-2xyy'=0
整理出y'即可

siny +e^x -xy^2=0
两侧对x求导数得到
cosy y' + e^x -y^2 -2xyy' =0
y' = (y^2-e^x)/(cosy -2xy)

dsiny+de^x-dxy²=0
cosydy+e^xdx-y²dx-2xydy=0
cosydy-2xydy=y²dx-e^xdx
dy/dx=(y²-e^x)/(cosy-2xy)