Difference Quotient

$\begin{displaymath} \Delta_h f(x) \equiv {f(x+h)-f(x)\over h} = {\Delta f\over h}. \end{displaymath}$

It gives the slope of the Secant Line passing through

and

. In the limit $n\to 0$ , the difference quotient becomes the Partial Derivative

$\begin{displaymath} \lim_{h\to 0} \Delta_{x(h)} f(x, y)={\partial f\over\partial x}. \end{displaymath}$