Letf be a function that is differentiable at a a E Reals, with f(a) not 0.

Define g(x)=1/f(x) for x near a. Prove that g is differentiable at a and give the formula for g'(a).

F(x) is differentiable at a implying it is continuos at a. So g(x) tends to 1/f(a) as x tends to a. g'(a) = lim((g(x)- g(a))/x-a)) = (1/f(x) - 1/f(a))/(x-a)

Not sure what the next steps are.