求反三角函数的导数y=rsinφ,φ=arcsin(y/r),求 dφ/dy.

y = r sinφ
dy/dφ = r cosφ
因为 sinφ = y/r,所以 cosφ = (1-(y/r)^2)^(1/2)
dφ/dy = 1 / (dy/dφ) = 1 / ( r cosφ)
= 1 / [ r*(1-(y/r)^2)^(1/2) ]