If [math]f[/math] is a function and [math]a[/math] is number in the domain of [math]f[/math], then the notation [math]f'\left(a\right)[/math] means the slope of the tangent line to the graph [math]y=f\left(x\right)[/math] through the point [math]\left(a,f\left(a\right)\right)[/math]. We call this "the derivative of [math]f[/math] at [math]a[/math]." By considering all the different values of [math]f'\left(a\right)[/math] as [math]a[/math] varies through the domain of [math]f[/math], we can construct "the derivative function" [math]f'\left(x\right)[/math].[br]