Tool for Second Derivative calculation f''. The second derivative is the application of the derivation tool to the (first) derivative of a function, a double derivation on the same variable.

Second Derivative - dCode

Tag(s) : Functions

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The **second derivative** (or second order derivative) is the application of the derivative on the first derivative of a function.

__Example:__ $$ f(x) = x^2+\sin(x) \Rightarrow f'(x) = 2 x+\cos(x) \Rightarrow f´´'x) = 2 - \sin(x) $$

In physics the **second derivative** is usually used for acceleration calculations

A **second derivative** can be written $ f´´ (x) $ or $ f^{(2)} (x) $ or $ \frac{d^2f}{dx^2} $. On dCode prefer `f ' '` which is the most used notation (and the fastest to write).

The **second derivative** is used to know the variation of the slope of the curve representing the function. For a given interval:

— a positive **second derivative** means an increase of the slope (convex function)

— a negative **second derivative** signifies a decrease in thought (concave function)

— a zero **second derivative** means a straight / straight curve

For a given point:

— a **second derivative** canceling with a change of sign means a point of inflection, the curvature of the graphical representation changes and is reversed. It is a stationnary point that can be a maximum of the function or a minimum of the function.

Any function that is non-continuous, and / or non-differentiable in at least one point, does not have a **second derivative**. See the tools definition domains of a function, and the derivative domain of a function.

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