Verified answer

[tex]\displaystyle\bf\\1)\\\\f(x)=\frac{x^{2} }{x-6}\\\\\\f'(x)=\frac{(x^{2} )'\cdot(x-6)-x^{2} \cdot(x-6)'}{(x-6)^{2} } =\frac{2x\cdot(x-6)-x^{2} }{(x-6)^{2} } =\\\\\\=\frac{2x^{2} -12x-x^{2} }{(x-6)^{2} } =\frac{x^{2} -12x}{(x-6)^{2} } \\\\\\f'(8)=\frac{8^{2}-12\cdot 8 }{(8-6)^{2} } =\frac{64-96}{4}=-8\\\\\\2)\\\\\\f(x)=(3x-7)^{5} \\\\\\f'(x)=5(3x-7)^{4} \cdot (3x-7)'=15(3x-7)^{4} \\\\\\f'(2)=15\cdot(3\cdot 2-7)^{4} =15\cdot 1=15 }[/tex]

[tex]\displaystyle\bf\\3)\\\\\\f(x)=\frac{16}{(x-2)^{2} } =16\cdot(x-2)^{-2} \\\\\\f'(x)=16\cdot (-2)(x-2)^{-3} =-\frac{32}{(x-2)^{3} } \\\\\\f'(4)=-\frac{32}{(4-2)^{3} }=-\frac{32}{8}=-4[/tex]