(2) x*tan(y)=1
d(x*tan(y))/dx = d(1)/dx
tan(y)+x*(cos(y))^(-2)*dy/dx = 0
dy/dx = -tan(y)*(cos(y))^2/x
tan(y)=1/x より　cos(y)=x/√(x^2+1)
dy/dx = - 1/x * x^2/(x^2+1) * 1/x = - 1/(x^2+1)
間違ってるかもしれないけど考え方はこんな感じでいいんじゃね