方程y=tan(x-y)所确定的函数的二阶导数

Question

拜托，，，

Answer 1

 

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Answer 2

y'=sec²(x-y)*(x-y)'
y'=sec²(x-y)*(1-y')=sec²(x-y)-sec²(x-y)*y'
y'=sec²(x-y)/[1+sec²(x-y)]=1-1/[1+sec²(x-y)]

所以
y''=-1*{-1/[1+sec²(x-y)]²}*[1+sec²(x-y)]'
=1/[1+sec²(x-y)]²*2sec(x-y)*tan(x-y)sec(x-y)*(x-y)'
=1/[1+sec²(x-y)]²*2sec²(x-y)*tan(x-y)*(1-y')
=2sec²(x-y)*tan(x-y)/[1+sec²(x-y)]²*{1-sec²(x-y)/[1+sec²(x-y)]}
=2sec²(x-y)*tan(x-y)/[1+sec²(x-y)]³

Answer 3