script52.py

Created on January 18, 2022
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#Fonction Logarithme Décimal

Particularité

log1 = 0
log10 = 1
log1/10 = -1
log10^x = x
10^logx = x 

Propriétés de la fonction logarithme décimale :

log( a * b ) = loga + logb
loga^n = nloga
loga/b = loga- logb
log1/b = -logb

loga = b
e^loga = e^b
a = e^b

#Fonction Logarithme Népérien

Pour x > 0 :
y = lnx <=> e^y = x
ln1 = 0
lne = 1
ln1/e = -1
lne^x = x
e^lnx = x

ln( a * b ) = lna + lnb
lna^n = nlna
lna/b = lna - lnb
ln1/b = -lnb
ln'racine de a' = 1/2 * lna
(lnx)' = 1/x

a^m * a^n = a^m+n
a^m / a^n = a^m-n
(a^m)^n = a^m*n
a^-n = 1 / a^n
e^a = e^b   <=>   a = b
e^a > e^b   <=>   a > b

f(x)= a ->f'(x)= 0
f(x)= ax ->f'(x)= a
f(x)= x^n ->f'(x)=nx^n-1
f(x)= 1/x ->f'(x)= - 1/x^2
f(x)= cos(x) ->f'(x)=-sin(x)
f(x)= sin(x) ->f'(x)=cos(x)
f(x)= (u + v)' ->f'(x)= u' + v'
f(x)= (coef*u)' ->f'(x)= ku'
f(x)= (uv)' ->f'(x)= u'v + uv'
f(x)= (1/u)' ->f'(x)= - u'/u^2
f(x)= (u/v)'->f'(x)= (u'v - uv')/v**2
f(x)= Acos(ax+phi) ->f'(x)= -Aasin(ax+phi)
f(x)= Asin(ax+phi) ->f'(x)= Aacos(ax+phi)
f(x)= f(ax + b) ->f'(x)= a*f'(ax + b)

  II.

  Tangente en a :
  
  y = f'(a)*(x-a) + f(a)
  
  Calcule de f(x)' et de f(x)
  puis tu remplace les x par a.
  :
         
f(x)= u^n ->f'(x)= nu'u^n-1
f(x)= e^u ->f'(x)= u'e^u
f(x)= ln(u) ->f'(x)= u'/u
f(x)= cos(u) ->f'(x)= -u'sin(u)
f(x)= sin(u) ->f'(x)= u'cos(u)