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*!

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.

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.

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 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 source code of the script Second Derivative online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Second Derivative script for offline use on PC, iPhone or Android, ask for price quote on contact page !

derivative,second,function,differentiation,calculator,acceleration

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

© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback

▲