Question 1180615


{{{f(x)= 10e^x-e*x^e}}}

Find {{{f}}}'{{{(3)}}}

first find {{{f}}}'{{{(x)}}}


{{{(d/dx)(10e^x-e*x^e)}}}.......apply the Sum/Difference Rule

={{{(d/dx)(10e^x)-(d/dx)(e*x^e)}}}....factor constant out

={{{10(d/dx)(e^x)-e(d/dx)(x^e)}}}

={{{10e^x-e^2*x^(e-1)}}}


{{{f}}}'{{{(x) = 10e^x - e^2*x^(e - 1)}}}

then

{{{f}}}'{{{(3) = 10e^3 - e^2*3^(e - 1)}}}
{{{f}}}'{{{(3) = 152.05}}}