Limit Definition of the Derivative

$f^{\prime }(x)={\lim }_{dx\to 0}\frac{f(x+dx)-f(x)}{dx}$

Basically, it’s the slope $f^{\prime }(x)=\frac{\text{rise}}{\text{run}}$

• d means derivative, I originally thought it meant delta
• so we come about this equation by imagining two points (let’s say P and Q) on f(x) and we want to bring point Q to P we do this by bringing Q’s x which is delta x closer to x (P’s x). Doing this we’ll eventually get the slope of the tangent line at x
• this is literally just Rise over Run