Some Random Garbage Follows. These aren't the droids you're looking for.
lim Δ x → 0 f ( x + Δ x ) − f ( x ) Δ x {\displaystyle {\underset {\Delta x\to 0}{\mathop {\lim } }}\,{\frac {f\left(x+\Delta x\right)-f\left(x\right)}{\Delta x}}}