设函数y＝f(x)由方程cos(xy)＋lny－x＝1确定，求dy／dx
答案:2 悬赏:30
解决时间 2021-11-05 00:28
- 提问者网友：兔牙战士
- 2021-11-04 19:56
设函数y＝f(x)由方程cos(xy)＋lny－x＝1确定，求dy／dx
最佳答案
- 二级知识专家网友：迟山
- 2021-11-04 21:15
dcos(xy)+dlny-dx=d(1)
-sin(xy)d(xy)+(1/y)dy-1=0
-sin(xy)(xdy+ydx)+(1/y)dy-1=0
-xsin(xy)dy-ysin(xy)dx+(1/y)dy-1=0
所以dy/dx=[ysin(xy)+1]/[1/y-xsin(xy)]
=[y²sin(xy)+y]/[1-xysin(xy)]
-sin(xy)d(xy)+(1/y)dy-1=0
-sin(xy)(xdy+ydx)+(1/y)dy-1=0
-xsin(xy)dy-ysin(xy)dx+(1/y)dy-1=0
所以dy/dx=[ysin(xy)+1]/[1/y-xsin(xy)]
=[y²sin(xy)+y]/[1-xysin(xy)]
全部回答
- 1楼网友：夜风逐马
- 2021-11-04 21:57
y'=y-1+y^2×sin(xy)／-xysin(xy)
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