Search for a tool
Derivative

Tool to compute derivatives. The differentiation is a fundamental tool when analyzing a function, it allows to measure the sensitivity to change of a function.

Results

Derivative -

Tag(s) : Functions

Share
Share
dCode and you

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 community Discord for help requests!


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

Derivative

Sponsored ads

Derivative Calculator



Tool to compute derivatives. The differentiation is a fundamental tool when analyzing a function, it allows to measure the sensitivity to change of a function.

Answers to Questions

What is a derivative? (Definition)

Mathematicians have defined derivatives by the formula $$ \frac{d}{dx}f = f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} $$

The derivative of a function $ f $ is denoted $ f' $ (with an apostrophe named prime) or $ \frac{d}{dx}f $ where $ d $ is the derivative operator and $ x $ the variable on which to derivate.

The derivative calculation is the inverse operation of primitive calculation (indefinite integral).

How to calculate a derivative?

The derivation calculation (first order derivative) is based mainly on a list of usual derivatives, already calculated and known (see below).

On dCode, the derivative calculator knows all the derivatives, indicate the function and the variables on which to derivate to obtain the result of the derivative computation.

Example: $$ f(x) = x^2+\sin(x) \Rightarrow f'(x) = 2 x+\cos(x) $$

Derivative calculus is often used in physics to compute a velocity.

What is the list of common derivatives?

The more useful derivatives are:

NameFunctionDerivative
constant$$ k \in \mathbb{R} $$$$ 0 $$
variable$$ x $$$$ 1 $$
power n$$ x^n $$$$ n x^{n-1} $$
negative power$$ x^{-n} $$$$ -n x^{-n-1} $$
fraction$$ \frac{1}{x} $$$$ -\frac{1}{x^2} $$
inverse power$$ \frac1{x^n} $$$$ -\frac n{x^{n+1}} $$
root$$ \sqrt{x} $$$$ \frac 1{2\sqrt{x}} $$
nth root$$ \sqrt[n]x $$$$ \frac1{n\sqrt[n]{x^{n-1}}} $$
fractional power$$ x^{1/n} $$$$ (1/n)x^{(1/n)-1} $$
natural logarithm$$ \ln |x| $$$$ \frac{1}{x} $$
logarithm base a$$ \log_a |x| $$$$ \frac{1}{x \ln a} $$
exponential$$ e^x $$$$ e^x $$
exponent$$ a^x $$$$ a^x \ln a $$
sinus$$ \sin x $$$$ \cos x $$
cosinus$$ \cos x $$$$ - \sin x $$
tangent$$ \tan x $$$$ \frac{1}{\cos^2 x} = 1+\tan^2 x $$
cotangent$$ \cot x $$$$ - \frac{1}{\sin^2 x} = -1-\cot^2 x $$
arcsinus$$ \arcsin x $$$$ \frac{1}{\sqrt{1-x^2}} $$
arccosinus$$ \arccos x $$$$ -\frac{1}{\sqrt{1-x^2}} $$
arctangent$$ \arctan x $$$$ \frac{1}{1+x^2} $$
sinus hyperbolic$$ \sinh x $$$$ \cosh x $$
cosinus hyperbolic$$ \cosh x $$$$ \sinh x $$
tangent hyperbolic$$ \tanh x $$$$ \frac{1}{\cosh^2 x} = 1 - \tanh^2 x $$
cotangent$$ \coth $$$$ \frac{-1}{\sinh^2 x} = 1 - \coth^2 x $$
arcsinus hyperbolic$$ \mathrm{arcsinh} x $$$$ \frac{1}{\sqrt{1+x^2}} $$
arccosinus hyperbolic$$ \mathrm{arccosh} x $$$$ \frac{1}{\sqrt{x^2-1}} $$
arctangent hyperbolic$$ \mathrm{arctanh} x $$$$ \frac{1}{1-x^2} $$

How to calculate a second derivative?

A second derivative is equivalent to compute the derivative twice, for dCode, indicate twice the same variable to get the second derivative.

Second derivative calculation is often used in physics to compute acceleration (derivative of velocity).

How to calculate a partial derivative?

A partial derivative is a derivative that only applies to one variable, leaving the others intact.

On dCode, indicate a single variable if the function has several to obtain a partial derivative.

How to calculate a primitive?

Use the primitive calculator tool available on dCode.

Source code

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

Need Help ?

Please, check our community Discord for help requests!

Questions / Comments

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


Source : https://www.dcode.fr/derivative
© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback