Search for a tool
Nth Derivative

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.

Results

Nth Derivative -

Tag(s) : Functions

Share
Share
dCode and more

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!


Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!


Feedback and suggestions are welcome so that dCode offers the best 'Nth Derivative' tool for free! Thank you!

Nth Derivative

Nth Derivative Calculator




Answers to Questions (FAQ)

How to calculate a nth derivative?

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

What can be a nth derivative for?

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.

How to write a nth derivative?

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.

Which functions have remarkable successive derivatives?

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

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

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

Source code

dCode retains ownership of the "Nth Derivative" source code. Except explicit open source licence (indicated Creative Commons / free), the "Nth Derivative" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, 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, or API access for "Nth Derivative" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.

Cite dCode

The copy-paste of the page "Nth Derivative" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Nth Derivative on dCode.fr [online website], retrieved on 2024-11-07, https://www.dcode.fr/nth-derivative

Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Feedback and suggestions are welcome so that dCode offers the best 'Nth Derivative' tool for free! Thank you!


https://www.dcode.fr/nth-derivative
© 2024 dCode — El 'kit de herramientas' definitivo para resolver todos los juegos/acertijos/geocaching/CTF.
 
Feedback