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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.

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Derivative -

Tag(s) : Mathematics

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Derivative

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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

How to calculate a derivative?

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 primitivehref calculation. dCode knows all derivatives, one has only to indicate the function and the deriving variable.

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$$ \arcsinh x $$$$ \frac{1}{\sqrt{1+x^2}} $$
arccosinus hyperbolic$$ \arccosh x $$$$ \frac{1}{\sqrt{x^2-1}} $$
arctangent hyperbolic$$ \arctanh x $$$$ \frac{1}{1-x^2} $$

How to calculate a second derivative?

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

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