How do I effectively calculate how much polynomial functions deviate from the actual polynomial of interest when the value of $x$ is changed by a small amount that is :
$$|f(x+\delta x)-f(x)|$$
Is there a nice formula or easy way to calculate this error gap for a given polynomial? Additionally is there a method to do the same for not only polynomial functions, but trigonometric functions in general as well such as $f(x) = a\sin (bx+c) $? I just want to compare like say trigonometric functions and polynomials and see which one has a larger error gap when the value if $x$ changes by a small amount.