Problem with differentiation as a concept. I don't understand quiet good something here, for example if we want to find the derivative of the function $\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(h)}{h} $ and if we compute it from the function: $ f(x) = 12 + 7x $
We get that the derivative of $f(x)$ is equal to $$\lim_{h \to 0} \frac{7h}{h}$$
But I thought that we can't divide by zero (here we cancel 0 over 0), I'm I wrong or $\displaystyle \frac{0}{0}$ equals 1? 

The whole point of the limit operation is that it avoids any bad behaviour of a function around the given point. We don't care what the function value is, nor whether it's even defined at a given point.
In your case, so long as $h \ne 0$, we can cancel to find that $\frac {7h}{h} = 7$; it doesn't matter that $\frac{7h}{h}$ isn't defined at $0$.
