The limitation of derivative of modified Bessel function of second kind

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The final result I draw is related to the derivation of modified Bessel function of the second kind. But I can not solve it. Are you willing to help me? Thank all

$I = \mathop {\lim }\limits_{x \to 0} \frac{\partial }{{\partial x}}\frac{{{K_0}(a\sqrt x )}}{{{K_0}(b\sqrt x )}}$ which a and b are real numbers