Exponential Functions

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• Misc
  • MLC calc 1 review
    • Thursday, Jan. 29, 6:00 - 7:30 PM
    • Newton 214
  • Math colloquium
    • “Solutions to Polynomials in Two Variables”
    • Dr. Tom Tucker, UR math dept.
    • Thursday Jan 29th, 5:00 - 6:00 PM
    • Newton 204
    • Extra Credit (equivalent to up to 2 points on a problem set) for going and writing a 1-paragraph summary
• Questions?
• Exponential Functions
  • Section 7.3
    • e^x (aka exp(x)) is inverse of ln x
      • ln( e^x ) = x
      • e^{ln x} = x
    • Exponential rules
      • e^xe^y = e^x+y
      • (e^x)^y = e^xy
    • Exponentiation
      • xⁿ means x times itself n times (integer n)
      • x^1/n means n-th root of x
      • (xⁿ)^m means x^nm
    • x = e^{ln x} means x^y = (e^{ln x})^y = e^{yln x}
    • log_bx = lnx / lnb
    • Derivative/anti-derivative rules
      • d/dx e^x = e^x
      • So antiderivative of e^x = e^x + C
      • d/dx a^x = lna a^x
        • Derivation: d/dx a^x
        • = d/dx (e^lna)^x
        • = d/dx e^xlna
        • = e^xlna (d/dx xlna)
        • = e^xlna lna
        • = (e^lna)^x lna
        • = a^x lna
      • Anti-derivative of a^x = (a^x / lna) + C
  • Examples
    • Integrals
      
    • Differentiate
      • d/dx (e^5x)
        • = 5 e^5x
• Next
  • Continue the exponential function

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