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