[tex]\displaystyle\bf\\1)\\\\g(x)=Sin6x+Cos3x\\\\g'(x)=(Sin6x)'+(Cos3x)'=6Cos6x-3Sin3x\\\\g'(x_{0} ==g'\Big(\frac{\pi }{3} \Big)=6Cos\Big(6\cdot\frac{\pi }{3} \Big)-3Sin\Big(3\cdot\frac{\pi }{3} \Big)=\\\\\\=6Cos2\pi -3Sin\pi =6\cdot 1-3\cdot 0=6\\\\2)\\\\g(x)=\sqrt{5x+1} -4tgx\\\\g'(x)=(\sqrt{5x+1)'} -4\cdot(tgx)'=\frac{5}{2\sqrt{5x+1} }-4\cdot\frac{1}{Cos^{2} x} \\\\\\g'(x_{0} )=g'(0)=\frac{5}{2\sqrt{5\cdot 0+1} } -\frac{4}{Cos^{2}0 }=\frac{5}{2} -4=-1,5[/tex]