Question

find f'(x) at the given value of x: f(x) = -1 / x+6

Answer 1

Consider f(x) as \[-1(x+6)^{-1}\] then it is simply a matter of bringing down the -1 in the exponent and changing it to -2 so:
\[f'(x)=\frac{ 1 }{ (x+6)^{2} } \]