Exponentielle

• Exponential function

  • For all real x and for all real y > 0, e^x = y <=> x = ln y

  For all real x, e^x > 0

  For all real x, ln(x) exists if and only if x > 0
• Exponential function base a

  For any real a > 0, for all real x, a^x = e^(x \* ln(a))
• Exponential function base a


  Function x 7→ a^x
• For any real a > 0, the function x 7→ a^x is derivable on R