>>583
(1/y)(dx/dy)=(-1/x^2)log(x)+(1/x)^2　= (x^(-2)) (1-log(x))
dx/dy = (x^((1/x)-2) (1-log(x))

(2)は、補助的に
y = arcsin(x)
x = sin(y)
dx/dy = cos(y) = √(1-x^2)
dy/dx = 1/√(1-x^2)
と求めた後、普通に積の微分