Given f(x) = (x+1)/x

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

Now using first principle,

     dy/dx = lim_h->0 [{f(x+h) - f(x)}/h]

=> dy/dx = lim_h->0 [{(x+h+1)/(x+h) - (x+1)/x}/h]

=> dy/dx = lim_h->0 [{(x+h+1)*x - (x+h)*(x+1)}/{h*x*(x+h)}]

=> dy/dx = lim_h->0 [{(x² + hx + x) - (x² + x + hx + h)}/{h*x*(x+h)}]

=> dy/dx = lim_h->0 [-h/{h*x*(x+h)}]

=> dy/dx = lim_h->0 [-1/{x*(x+h)}]

=> dy/dx = -1/{x*(x+0)}

=> dy/dx = -1/x²