Question

Use the definition of derivative: lim(as h approaches 0) (f(x+h)-f(x)/(h) to find

f(x)=(1)/(2x).

Answer 1

f(x+h) = 1/(2x+2h)

f(x) = 1/2x

f(x+h)-f(x)
= (2x -2x-2h)/2x(2x+2h)
= -2h/(4x^2+4xh)

divide by h
= -2/(4x^2+ 4xh)

let h--->0
= -2/4x^2

= -1/2x^2