试证明下列命题:
(1) $I = {\int }_{0}^{\pi /2}\frac{\mathrm{d}x}{{\left( {a}^{2}{\cos }^{2}x + {b}^{2}{\sin }^{2}x\right) }^{2}} = \frac{\pi \left( {{a}^{2} + {b}^{2}}\right) }{4\left| {{a}^{3}{b}^{3}}\right| }\left( {a,b > 0}\right)$ .
(2) 设 $f\left( x\right) = {\int }_{0}^{x}\cos \left( \frac{1}{t}\right) \mathrm{d}t$ ，则 ${f}^{\prime }\left( 0\right) = 0$ .