求详解y=tan(x+y)

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求详解y=tan(x+y)
求隐函数的二阶导数d²y/dx²

你要求什么?dy/dx?
1*dy/dx= sec²(x+y) *(dy/dx+1)
dy/dx(1-sec²(x+y))=sec²(x+y)
dy/dx(-tan²(x+y))=sec²(x+y)
dy/dx=-(1+tan²(x+y))/tan²(x+y)
dy/dx=-cot²(x+y)-1
d²y/dx²=cot(x+y)csc(x+y)(1+dy/dx)
=cot(x+y)csc(x+y)(-cot²(x+y))
=-cot³(x+y)csc(x+y)
再问：二导。
再答：刚刚有个地方错了cot²(x+y)处理失误，重来 d²y/dx²=-cot(x+y)csc(x+y){-2cot(x+y)}[1+dy/dx] =2cot²(x+y)csc(x+y)[-cot²(x+y)] =-2cot^4(x+y)csc(x+y)