The second derivative is simply the derivative of the first derivative.

The second derivative of a function is simply the derivative of the first derivative of the function.

We first calculate the first and second derivative of function f

(f' is the first derivative of f, f" is the second derivative etc.)

The second derivative of a function is simply the derivative of the first derivative of the function.

Compute the first and second partial derivatives of a function

This program calculates the first and second derivatives of a function.

The edge frequency estimation is preferably based on a ratio of a third to a first low-pass derivative of image signal.

Using the First Derivative Test to Find Local Extrema

The smoothstep function, with its first and second derivatives:

So this method, the first-derivative test, we consider the first derivative — that’s the gradient — either side of the critical point.

At either boundary the function and its first derivative are continuous.

This applet shows the graphs of a function f, its first derivative f', and its second derivative f''.

Below are shown the graph of function f, its first derivative f' and its second derivative f''.

Figure 3: Theorem 3: Function f, its first derivative f ' and its second derivative f ''.