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) = uv + 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)