如图所示,🙏
设u=arcsin(v),v=1/x所以dy/dx=(dy/du)(du/dv)(dv/dx)=f'(u)1/√(1-v^2)(-1/x^2)=-f'(arcsin1/x)/[x√(1-x^2)]
y'=(arcsin1/x)'f'(arcsin1/x)=(1/x)'/√(1-1/x²) f'(arcsin1/x)=(-1/x²)/√(1-1/x²) f'(arcsin1/x)=-f'(arcsin1/x)/[x√(x²-1)]