Question

Find dy/dx of the function f(x) =1/x from first principle

Answer 1

lim (h->0) [1/(x+h) - 1/x]/h

= lim(h->0) [x - (x+h)]/[hx(x+h)]
= lim(h->0) -h/[hx(x+h)]
= lim(h->0) -1/[x(x+h)]
= -1/x^2