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
f(x) = f '(x) = 1 / (n· n-1)
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
f(x) = arccos x
f(x) = arctan x
f(x) = arccotan x
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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