exponentielles.py

Created on December 04, 2023

632 Bytes

fonctions exponentielles 
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variations (x -> a**x) : 
  Si a > 1, a**x croissant sur R
  Si 1 > a > 0, a**x decroissant sur R
  Si a = 1, a**x constant sur R
  
Rappel puissances : 
  a**x * a**y = a**x+y
  a**x / a**y = a**x-y
  (a**x)**y = a**x*y
  a**x * b**x = (ab)**x
  a**x / b**x = (a/b)**x
  a**-x = 1/a**x
  a**1/2 = sqrt(a)
  
dérivée importante : 
(e**u(x)) = u'(x) e**u(x)
exemple : 
  e**(3x**(2)+5x)
  = (6x+5)e**(3x**(2)+5x)
  
formules derivees importantes :
  (u+v)' = u' + v'
  (ku)' = ku'
  (u*v)' = u'v * uv'
  (1/u)' = -u/u**2
  (u/v)' = u'v-uv'/v**2

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