Let f(x)=x9(x3)8(x2+6)6\displaystyle {f{{\left({x}\right)}}}=\frac{{{x}^{{{9}}}{\left({x}-{3}\right)}^{{{8}}}}}{{{\left({x}^{{2}}+{6}\right)}^{{{6}}}}}

Use logarithmic differentiation to determine the derivative.

f(x)=\displaystyle {f}'{\left({x}\right)}=