Question

Find from first principle, the derivative of 3/x with respect to x

Answer 1

if f(x) = 3/x then

df/dx = the limit of
(f(x+h)-f(x))/h
The numerator is
3/(x+h) - 3/x = (3x-3(x+h))/(x(x+h) = -3h/(x(x+h))
Now divide all that by h and you have -3/(x(x+h))
Now take the limit as h→0 and you have -3/x^2