derivation.py

Created by anaali
Created on April 02, 2024
896 Bytes
(1 / x)′ = -1 / x2
(1/x**n)′= -n / x**n+1
( sqrt(x) )′ = 1 / 2sqrt(x)
(u + v)′ = u′ + v′
(u − v)′ = u′ − v′
(k * u)′ = k * u′
(u * v)′ = u′v + uv′
(1 / v)′ = -v′/ v2
(u / v)′ = (u′* v− u * v′)/v2
g(ax+b)′ = a * g′(ax + b)
cos(u)=-sin(u)*u'
sin(u)=cos(u)*u'
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VoU=V(U(x))
f=VoU f'=U'=V'oU

f=sqrt(U) U>0
f'=U'/2sqrt(U)

f=(U)**n si n<0 U!=0
f'=nU'* U**n-1

f=e**U
f'=U'e**U
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f est convexe:
  f'  croissante
  f'' positive
pt inflexion:
f'' s'annule changeant signe
_______________________
continue si 
lim f(x)= lim f(x)=f(a)
x=>a      x=>a
x<a       x>a

relation recurence Un+1=f(Un)
pt fixe:
  f(I) appartient a I
  U0 appartient a I
  converge vers l
  f est continue
f(x)=x donne l
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Taux de variation
t(h)= (f(a+h)- f(a)) /h

Equation reduite de la tangente
y= f'(a)(x-a)+f(a)

Coef direct
(yB-yA)/ (xB-Xa)