Question

use the definition of derivative to find the derivative of f(x)=1/x+3

Answer 1

d(1/x+3)/dx=\[\lim_{DeltaX \rightarrow 0} (1/(x+Deltax)+3-(1/x+3))/Deltax\]
I'm dropping the lim, but remember it's still there
(x/(x+Deltax)(x)-(x+Deltax)/(x+Deltax)(x))/Deltax
-1/(x+Deltax)(x)
Now insert zero for the Deltax.
-1/x^2