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  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⋅ln(y)+x2y3.
  • z″xx(x,y)=ln(y)+2xy3
  • z″yy(x,y)=xy+3x2y2
  • z″xx(x,y)=2y3
  • z″yy(x,y)=−xy2+6x2y
None of the other answers is correct.
  • z″xx(x,y)=ln(y)+2y3
  • z″yy(x,y)=1y+6x2y
Determine z″xx(x,y) and z″yy of z(x,y)=x⋅ln(y)+x2y3.
Antwoord 1 correct
Correct
Antwoord 2 optie
  • z″xx(x,y)=ln(y)+2xy3
  • z″yy(x,y)=xy+3x2y2
Antwoord 2 correct
Fout
Antwoord 3 optie
  • z″xx(x,y)=ln(y)+2y3
  • z″yy(x,y)=1y+6x2y
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)=2y3
  • z″yy(x,y)=−xy2+6x2y
Antwoord 1 feedback
Correct:
  • z′x(x,y)=ln(y)+2xy3
  • z′y(x,y)=xy+3x2y2
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)=ln(y)+2xy3.

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

Try again.