求问第三题打勾的两道题怎么做
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(1)两边对x求导,2x-2ydy/dx=0
dy/dx=x/y
d2y/dx2=(y-xdy/dx)/y^2=(y-x^2/y)/y^2=(y^2-x^2)/y^3
(3)两边对x求导,dy/dx=sec^2(x+y)*(1+dy/dx)
dy/dx=sec^2(x+y)/[1-sec^2(x+y)]=-sec^2(x+y)/tan^2(x+y)=-csc^2(x+y)
d2y/dx2=-2csc(x+y)*[-cot(x+y)csc(x+y)]*(1+dy/dx)=-2csc^2(x+y)*cot^2(x+y)
dy/dx=x/y
d2y/dx2=(y-xdy/dx)/y^2=(y-x^2/y)/y^2=(y^2-x^2)/y^3
(3)两边对x求导,dy/dx=sec^2(x+y)*(1+dy/dx)
dy/dx=sec^2(x+y)/[1-sec^2(x+y)]=-sec^2(x+y)/tan^2(x+y)=-csc^2(x+y)
d2y/dx2=-2csc(x+y)*[-cot(x+y)csc(x+y)]*(1+dy/dx)=-2csc^2(x+y)*cot^2(x+y)
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