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[ begin{array}{l} fleft(frac{pi}{6} ight)=9 f^{prime}left(frac{pi}{6} ight)=-15 g(x)=f(x) cos (x), text { and } h(x)=frac{sin (x)}{f(x)} . end{array} ] Find ( g^{prime}left(frac{pi}{6} ight)
\\[ \\begin{array}{l} f\\left(\\frac{\\pi}{6}\ ight)=9 \\\\ f^{\\prime}\\left(\\frac{\\pi}{6}\ ight)=-15 \\\\ g(x)=f(x) \\cos (x), \\text { and } \\\\ h(x)=\\frac{\\sin (x)}{f(x)} . \\end{array} \\] Find \\( g^{\\prime}\\left(\\frac{\\pi}{6}\ ight) \\) and \\( h^{\\prime}\\left(\\frac{\\pi}{6}\ ight) \\) (no rounding, give exact answers). \\[ \\begin{array}{l} g^{\\prime}\\left(\\frac{\\pi}{6}\ ight)= \\\\ h^{\\prime}\\left(\\frac{\\pi}{6}\ ight)= \\end{array} \\]
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