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

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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. To download the online Derivative script for offline use on PC, iPhone or Android, ask for price quote on contact page !

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

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