Question

We want f'(9) if f(x) = 1/sqrt(x). Using the definition of the derivative.

Answer 1

f(x) also can be written as:
\[f(x)= x ^{-1/2}\]

therefore: \[f'(x)= (-1/2)*1/(x ^{3/2})\]

then, to get f'(9), just substitute x=9 into the equation above.