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

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

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.

dCode retains ownership of the online 'Second Derivative' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Second Derivative' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Second Derivative' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Second Derivative' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

Please, check our dCode Discord community for help requests!

NB: for encrypted messages, test our automatic cipher identifier!

derivative,second,function,differentiation,calculator,acceleration

Source : https://www.dcode.fr/second-derivative

© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback

▲
Thanks to your feedback and relevant comments, dCode has developed the best 'Second Derivative' tool, so feel free to write! Thank you!