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y=cos(xy),求y'

题目详情
y=cos(xy),求y'
▼优质解答
答案和解析
y`=-sin(xy)(y+xy`)
=-ysin(xy)-xy`sin(xy)
y`+xy`sin(xy)=-ysin(xy)
[1+xsin(xy)]y`=-ysin(xy)=-cos(xy)sin(xy)=-1/2sin2xy
y`=(-1/2sin2xy)/[1+xsin(xy)]