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  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization functions of two variables
  5. Second-order partial derivatives
  6. Example (film)

Example (film)

We determine the second-order partial derivatives of $z(x,y)=ye^x+x^2y-5x$.

  • $z'_x(x,y)=ye^x+2xy-5$
  • $z'_y(x,y)=e^x+x^2$

Hence,

  • $z''_{xx}(x,y)=ye^x+2y$
  • $z''_{yx}(x,y)=e^x+2x$
  • $z''_{xy}(x,y)=e^x+2x$
  • $z''_{yy}(x,y)=0$
‹ Vorige paginaSecond-order partial derivatives
Volgende paginaExercise 1 ›
Wiskunde Mathematics for business economics leeromgeving

 

  • Chapter 1: Functions of one variable
  • Chapter 2: Differentiation of functions of one variable
  • Chapter 3: Functions of two variables
  • Chapter 4: Differentiation of functions of two variables
  • Chapter 5: Optimization
    • Optimization functions of one variable
    • Applications 1
    • Optimization functions of two variables
      • Minimum/maximum
      • Stationary point
      • First-order condition extremum
      • Second-order partial derivatives
        • Example (film)
        • Exercise 1
        • Exercise 2
        • Exercise 3
      • Second-order condition extremum
    • Applications 2
    • Optimization constrained extremum problems
    • Applications 3
    • Optimization convex/concave functions
  • Chapter 6: Areas and integrals

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