On the meaning of the second derivative When we want to find the velocity of an object we use the derivative to find this. However, I just learned that when you find the acceleration of the object you find the second derivative. 
I'm confused on what is being defined as the parameters of acceleration. I always thought acceleration of an object is it's velocity (d/t). 
Furthermore, in the second derivative are we using the x value or the y value of interest. In the first derivative we were only concerned with the x value. Does this still hold true with the second derivative?
I would post pictures but apparently I'm still lacking 4 points. 

Let $f(x)$ be a twice differentiable function.
Then, $f'(x)$ gives us the instantaneous rate of change of the function $f(x)$ at $x$ and $f''(x)$ gives us the instantaneous rate of change of the function $f'(x)$ at $x$.
If $f(x)$ happens to be a displacement function (say of a particle), then $f'(x)$ describes the velocity of that particle at $x$ and $f''(x)$ gives us its acceleration at that instant. Incidentally, if $f'''(x)$ exists, then it is a measure of what we call jerk.  
