cours_prim_deriv.py

Created on January 14, 2025
1.65 KB
from math import sin, cos, exp, log

def afficher_cours():
    """
    Affiche un cours sur les dérivees et primitives.
    """
    print("=== COURS : Derivees et Primitives ===")
    print("\n--- Les derivees ---")
    print("1. (u + v)' = u' + v'")
    print("2. (u*v)' = u'*v + u*v'")
    print("3. (u/v)' = (u'*v - u*v') / v^2")
    print("\nDérivées des fonctions courantes :")
    print(" - x       => 1")
    print(" - x^n     => n*x^(n-1)")
    print(" - ln(x)   => 1/x (x > 0)")
    print(" - e^x     => e^x")
    print(" - sin(x)  => cos(x)")
    print(" - cos(x)  => -sin(x)")
    print(" u^n ; n∈N => nu^(n-1)*u'")
    print(" 1/u^n     => (-n/u^(2+1))*u'")
    print(" racine(u) => (1/2rac(u))*u'")
    print(" ln(u)     => (1/u) *u'")
    print(" e^u       => e^u *u'")
    print(" sin(u)    => cos(u)×u'")
    print(" cos(u)    => -sin(u)×u'")
    print("\n--- Les primitives ---")
    print("1. ∫ (u + v) dx = ∫ u dx + ∫ v dx")
    print("2. ∫ (a*u) dx = a * ∫ u dx (a est une constante)")
    print("\nPrimitives des fonctions courantes :")
    print(" - x^n     => x^(n+1)/(n+1) ; (n ≠ -1)")
    print(" - 1/x     => ln(|x|)")
    print(" - e^x     => e^x")
    print(" - sin(x)  => -cos(x)")
    print(" - cos(x)  => sin(x)")
    print(" - a*u^n   => a*u^(n+1)/(n+1) ; (n ≠ -1)")
    print(" u'*u^n    => (1/n+1) *u^(n+1)")
    print(" u'/u^n    => -1/((n-1)*u^(n-1))")
    print(" u'/u      => ln(u)")
    print(" u'/u^2    => -1/u")
    print(" u'/rac(u) => 2rac(u)")
    print(" u'e^u     => e^u")
    print(" u'sin(u)  => -cos(u)")
    print(" u'cos(u)  => sin(u)")
    

def main():
    afficher_cours()
   

# Lancer le programme
main()