Question 1153268

Find {{{f}}} '{{{(a)}}}.

{{{f(t) = (2t + 4)/(t + 9)}}}


first find {{{f}}} '{{{(t)}}}


{{{(d/dt) (2t + 4)/(t + 9)}}}


Apply the Quotient Rule:


{{{(f/g)}}}' =({{{f}}}'*{{{g}}}-{{{g}}}'*{{{f}}})/{{{g^2}}}


={{{((d/dt)(2t+4)(t+9)-(d/dt)(t+9)(2t+4))/(t+9)^2}}}

since {{{(d/dt)(2t+4)=2}}} and {{{(d/dt)(t+9)=1}}}, we have

={{{(2(t+9)-(2t+4))/(t+9)^2}}}

={{{(2t+18-2t-4)/(t+9)^2}}}

={{{14/(t+9)^2}}}


{{{f}}}'{{{(t) = 14/(t + 9)^2}}}

then {{{f}}} '{{{(a)}}}:

{{{f}}}'{{{(a) = 14/(a + 9)^2}}}