求由方程cos(xy)=x^2*y^2 所确定的y的微分

问题描述:

求由方程cos(xy)=x^2*y^2 所确定的y的微分
1个回答 分类:数学 2014-10-25

问题解答:

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-sin(xy)[ydx+xdy]=2xy^2*dx+x^2*2ydy
-sin(xy)ydx-sin(xy)xdy=2xy^2*dx+2x^2*ydy
-2x^2*ydy-sin(xy)xdy=2xy^2*dx+sin(xy)ydx
-[2x^2*y+sin(xy)x]dy=[2xy^2+sin(xy)y]dx
dy/dx=-[2xy^2+sin(xy)y]/[2x^2*y+sin(xy)x]
 
 
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