using the limit definitiion of the derivative, whats the derivative of g(x) = 1/x?

Answer 1

g'(x) = lim [g(x + delta x) - g(x)] / delta x for delta x approaches 0
[1 / (x + delta x) - 1 / x ] / delta x
[x / x(x + delta x) - (x + delta x) / x(x + delta x)] / delta x
-delta x / (x^2 + x * deltax) / delta x
= lim -1 / (x^2 + x * deltax) as delta x approaches 0
= -1 / x^2

Answer 2

the derivative of 1/x is...e^x isn't it?