the derivative is a measure of how a function changes as its input changes.(from Wikipedia)
for instance, for function $y = x^2$ derivative y'= 2x, hence \begin{align*} x&= 6,&\quad y &=36,&\quad y'&= 12;\\ x&= 7,& y &=49,& y'&= 14;\\ x&= 8,& y &=64,& y'&= 16;\\ x&= 9,& y &=81,& y'&= 18;\\ x&= 10,& y &=100,& y'&= 20. \end{align*} In this case, intervals between two consecutive output values are roughly equal to corresponding y'.
But for function $y= x^3$, derivative y'= 3x^2, hence \begin{align*} x&= 1,&\quad y &=1,&\quad y'&= 3;\\ x&= 2,& y &=8,& y'&= 12; \\ x&= 3,& y &=27,& y'&= 27;\\ x&= 4,& y &=64,& y'&= 48;\\ x&= 5,& y &=125,& y'&= 75; \end{align*}
But here intervals between two consecutive output values are not at all equal to corresponding y'.
What's wrong? Did I understand "change in $y$ with respect to $x$" incorrectly?
What is the best way to understand "measure of how a function changes as its input changes"?