Question 1154502
{{{f(x) = x*sqr(9-x^2)}}} 

to find {{{f}}}'{{{(x)}}}  apply the Product Rule : {{{(f* g )}}}'={{{f}}} '*{{{g}}}+{{{f* g}}}'


{{{f}}}'{{{(x)}}}={{{(d/dx)x*sqrt(9 - x^2)+x* (d/dx)sqrt(9 - x^2)}}}


{{{f}}}'{{{(x)}}}={{{1*sqrt(9 - x^2)+x* (d/dx)sqrt(9 - x^2)}}}.......{{{(sqrt(9-x^2))}}}' ={{{- x/(sqrt(9-x^2))}}}


{{{f}}}'{{{(x)}}}={{{1*sqrt(9 - x^2)+x* (- x/(sqrt(9-x^2)))}}}


{{{f}}}'{{{(x)}}}= {{{sqrt(9 - x^2)- x^2/(sqrt(9-x^2))}}}


{{{f}}}'{{{(x)}}}= {{{(sqrt(9 - x^2))^2/(sqrt(9-x^2))- x^2/(sqrt(9-x^2))}}}


{{{f}}}'{{{(x)}}}= {{{(9 - x^2- x^2)/(sqrt(9-x^2))}}}


{{{f}}}'{{{(x)}}}= {{{(9 - 2x^2)/(sqrt(9-x^2))}}}