deriv.py

Created by egenspergersara

Created on February 06, 2024

903 Bytes


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Taux de variation : 
t(h)=f(a+h)-f(a)
     ----------
         h
lim t(h) = f'(a)
h->0

fonctions usuelles : 

constante k -> f'(x) = 0
affine ax+b -> f'(x) = a
carré x**2 -> f'(x) = 2x
puissance x**n -> f'(x) = nx**n-1
inverse 1 -> f'(x) = -1
       ---          ----
        x           x**2
racine carré Vx -> 1
                  ---
                  2Vx
                  
Equation : y = mx + p 
coeff directeur est f'(x)

Dérivée d'un produit u x v :
u'(x) x v(x) + u(x) x v'(x)

Dérivée d'un quotient u  :
                     ---
                      v
                      
u'(x) x v(x) - u(x) x v'(x)
---------------------------
        (v(x))**2

Dérivée d'un quotient 1  :
                    ---
                     v
 - v'(x)
 -------
(v(x))**2

Dérivée d'une somme : 
u'(x) = v'(x)

Dérivée d'un produit par un
nombre réel : 
k x u'(x)

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