math is fun

I was yesterday doing some basic differential calculus and so here I shall share it.
f(x) = 1/x
f'(x) = d/dx * 1/x
= [1/(x+h) - 1/x]/h
= [x/(x(x+h)) - (x+h)/(x(x+h))]/h
= [(x-(x+h)) / (x(x+h))] /h
= -h / (x(x+h)) / h
= -1/(x^2+hx)

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

f'(x) = d/dx * 1/x = -1/x^2

yay.