Tool for Nth Derivative calculation f^(n), so 1,2,3 or n times the application of the derivation to a function, a n-tuple iterated/successive derivation on the same variable.

Nth 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 nth derivative (or derivative of order $ n $) of a function $ f $ consists of the application of the derivative iteratively $ n $ times on the function $ f $.

__Example:__ $$ f(x) = x^4+\cos(x) \\ \Rightarrow f´(x) = 4 x^3-\sin(x) \\ \Rightarrow f´´(x) = 12x^2-\cos(x) \\ \Rightarrow f´´´(x) = 24x+\sin(x) \\ \Rightarrow f´´´´(x) = 24+\cos(x) $$

In physics, derivatives are useful for describing systems, the first derivative of a trajectory with respect to time represents speed, the second derivative represents acceleration and the third derivative characterizes jerk.

An nth derivative can be written either $ f^{(n)}(x) $ or $ \frac{d^n f}{dx^n} $.

When $ n $ is small (and is 1, 2 or 3), it is common to write a *prime* (an apostrophe) `f'` for the derivative, `f' '` for the second derivative, `f ' ' '` for the third derivative, etc.

The trigonometric functions $ \sin $ and $ \cos $ have successive periodic derivatives.

$$ f^{(4n)}(x) = \cos(x) \\ f^{(4n + 1)} (x) = -\sin (x) \\ f^{(4n + 2)} (x) = -\cos (x) \\ f^{(4n + 3)} (x) = \sin (x) $$

$$ f^{(4n)}(x) = \sin(x) \\ f^{(4n + 1)} (x) = \cos (x) \\ f^{(4n + 2)} (x) = -\sin (x) \\ f^{(4n + 3)} (x) = -\cos (x) $$

dCode retains ownership of the online "Nth Derivative" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Nth Derivative" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Nth Derivative" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, copy-paste, or API access for "Nth Derivative" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.

Please, check our dCode Discord community for help requests!

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

derivative,nth,function,differentiation,successive,iterated,calculator

Source : https://www.dcode.fr/nth-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 'Nth Derivative' tool, so feel free to write! Thank you!