Let \( f \) be a differentiable function in \( (0, \pi / 2) \). If \( \int_{\cos x}^{1} t^{2} f(...

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Let \( f \) be a differentiable function in \( (0, \pi / 2) \). If \( \int_{\cos x}^{1} t^{2} f(t) d t=\sin ^{3} x+\cos x \), then \( \frac{1}{\sqrt{3}} f^{\prime}\left(\frac{1}{\sqrt{3}}\right) \) is equal to
(a) \( 6-9 \sqrt{2} \)
(b) \( 6-\frac{9}{\sqrt{2}} \)
(c) \( \frac{9}{2}-6 \sqrt{2} \)
(d) \( \frac{9}{\sqrt{2}}-6 \)
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