n-1)
Dérivées de quelques fonctions élémentaires
| Fonction : | Dérivée première : | ||
| f(x) = k | f '(x) = 0 | ||
| f(x) = x | f '(x) = 1 | ||
| f(x) = ax + b | f '(x) = a | ||
| f(x) = xn | f '(x) = n· xn-1 | ||
| f(x) = |
f '(x) = 1 / 2 |
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| f(x) = |
f '(x) = 1 / (n·
n-1) |
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| f(x) = ax | f '(x) = ax· ln a | ||
| f(x) = ex | f '(x) = ex | ||
| f(x) = loga x | f '(x) = (1 / x)· loga e | ||
| f(x) = ln x | f '(x) = 1 / x | ||
| f(x) = log x | f '(x) = (1 / x)· log e | ||
| f(x) = sin x | f '(x) = cos x | ||
| f(x) = cos x | f '(x) = -sin x | ||
| f(x) = tan x | f '(x) = 1 / cos2 x = 1 + tan2 x | ||
| f(x) = cotan x | f '(x) = -1 / sin2 x = -(1 + tan2 x) | ||
| f(x) = arcsin x | |
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| f(x) = arccos x | |
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| f(x) = arctan x | |
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| f(x) = arccotan x | |
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| f(x) = sinh x | f '(x) = cosh x | ||
| f(x) = cosh x | f '(x) = sinh x | ||
| f(x) = tanh x | f '(x) = 1 / cosh2 x | ||
| f(x) = cotanh x | f '(x) = -1 / sinh2 x | ||
| f(x) = arcsinh x | |
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