Question

from the first principles,find the deriviative of 3/x with espect to x

Answer 1

dy/dx = lim ( f(x+h) - f(x) )/h , as h ---> 0

= lim (3/(x+h) - 3/x)/h
= lim [ (3x - 3x - 3h)/(x(x+h)) ]/h
= lim [-3h/(x(x+h)) ]/h
= lim -3/(x(x+h) , as h ---> 0
= -3/(x(x+0))
= -3/x^2