设siny+e的x次方-xy²=0,求dy/dx
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![设siny+e的x次方-xy²=0,求dy/dx](/uploads/image/z/4347580-4-0.jpg?t=%E8%AE%BEsiny%2Be%E7%9A%84x%E6%AC%A1%E6%96%B9-xy%26%23178%3B%3D0%2C%E6%B1%82dy%2Fdx)
设siny+e的x次方-xy²=0,求dy/dx
设siny+e的x次方-xy²=0,求dy/dx
设siny+e的x次方-xy²=0,求dy/dx
dsiny+de^x-dxy²=0
cosydy+e^xdx-y²dx-2xydy=0
cosydy-2xydy=y²dx-e^xdx
dy/dx=(y²-e^x)/(cosy-2xy)
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)
siny+e的x次方-xy²=0
y'cosy+e^x-y^2-2xyy'=0
整理出y'即可