Prove formula from Slide $10$:

$\frac{\text{d}\text{e}\text{l}\text{f}(x)}{\text{d}\text{e}\text{l}\text{x}}=f^{\text{'}}(x)=\frac{f(x+1)-f(x-1)}{2}$

$(basedon$ the previous two formulas from slide $10.)$

The two formulas are shown below.