1. Home
  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization functions of two variables
  5. Second-order partial derivatives
  6. Exercise 1

Exercise 1

Determine $z''_{xx}(x,y)$ and $z''_{yy}$ of $z(x,y)=x\cdot \textrm{ln}(y)+x^2y^3$.
  • $z''_{xx}(x,y)=2y^3$
  • $z''_{yy}(x,y)=-\dfrac{x}{y^2}+6x^2y$
  • $z''_{xx}(x,y)=\textrm{ln}(y)+2xy^3$
  • $z''_{yy}(x,y)=\dfrac{x}{y}+3x^2y^2$
  • $z''_{xx}(x,y)=\textrm{ln}(y)+2y^3$
  • $z''_{yy}(x,y)=\dfrac{1}{y}+6x^2y$
None of the other answers is correct.
Determine $z''_{xx}(x,y)$ and $z''_{yy}$ of $z(x,y)=x\cdot \textrm{ln}(y)+x^2y^3$.
Antwoord 1 correct
Correct
Antwoord 2 optie
  • $z''_{xx}(x,y)=\textrm{ln}(y)+2xy^3$
  • $z''_{yy}(x,y)=\dfrac{x}{y}+3x^2y^2$
Antwoord 2 correct
Fout
Antwoord 3 optie
  • $z''_{xx}(x,y)=\textrm{ln}(y)+2y^3$
  • $z''_{yy}(x,y)=\dfrac{1}{y}+6x^2y$
Antwoord 3 correct
Fout
Antwoord 4 optie
None of the other answers is correct.
Antwoord 4 correct
Fout
Antwoord 1 optie
  • $z''_{xx}(x,y)=2y^3$
  • $z''_{yy}(x,y)=-\dfrac{x}{y^2}+6x^2y$
Antwoord 1 feedback
Correct:
  • $z'_x(x,y)=\textrm{ln}(y)+2xy^3$
  • $z'_y(x,y)=\dfrac{x}{y}+3x^2y^2$
Go on.
Antwoord 2 feedback
Wrong: We do not want to know the first-order partial derivatives.

See Second-order partial derivative.
Antwoord 3 feedback
Wrong: $z'_x(x,y)=\textrm{ln}(y)+2xy^3$.

Try again.
Antwoord 4 feedback
Wrong: The correct answer is given.

Try again.