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.

Derivative - dCode

Tag(s) : Mathematics

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

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

Sponsored ads

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.

Mathematicians have defined derivatives using the formula $$ \frac{d}{dx}f = f\'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} $$ The derivative calculation is the inverse operation of primitive calculation. dCode knows all derivatives, indicate the function and the deriving variable to get the calculation result.

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

The more useful derivatives are:

Name | Function | Derivative |
---|---|---|

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 | $$ \mathrm{arctanh} x $$ | $$ \frac{1}{1-x^2} $$ |

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

Use the primitive calculator tool available on dCode.

dCode retains ownership of the source code of the script 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 given for free. So if you need to download the online Derivative script for offline use, check contact page !

derivative,function,differentiation,calculator,integrate,velocity,acceleration

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

© 2018 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback