高等数学习题一道

来源：百度知道 编辑：UC知道 时间：2024/06/16 19:25:33
求下列方程所确定的隐函数y的导数dy/dx.
xsiny=cos(x+y)
答案是:-sin(x+y)-siny/xcosy+sin(x+y),要过程.

方程两边求微分得
d(xsiny)＝dcos(x+y)
sinydx＋xdsiny＝－sin(x+y)d(x+y)
sinydx＋xcosydy＝－sin(x+y)(dx＋dy)
解得dy＝[-sin(x+y)-siny]dx/[xcosy+sin(x+y)]
所以，dy/dx＝[-sin(x+y)-siny]/[xcosy+sin(x+y)]

解：方程两边对x求导数：siny+x*cosy*(dy/dx)=-sin(x+y) ====> dy/dx=[-sin(x+y)-siny]/x*cosy