Exercise 3 | Wiskunde op Tilburg University

Consider the function

$z(x,y)=\;^3\!\log (x^3y^4)$ . Determine

$z''_{xy}(x,y)$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$z''_{xy}(x,y)=\dfrac{3}{x \textrm{ln}(3)}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$z''_{xy}(x,y)=\dfrac{4}{y\textrm{ln}(4)}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$z''_{xy}(x,y)=\dfrac{-4}{x^3y^4\textrm{ln}(3)}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$z''_{xy}(x,y)=0$

Antwoord 1 feedback

Correct:

$z'_x(x,y)=\dfrac{3x^2y^4}{x^3y^4\textrm{ln}(3)}=\dfrac{3}{x\textrm{ln}(3)}$ . Hence,

$z''_{xy}=z''_{yx}(x,y)=0$ .

Go on.

Antwoord 2 feedback

Wrong:

$z''_{xy}(x,y)\neq z'_x(x,y)$ .

See Second-order partial derivatives.

Antwoord 3 feedback

Wrong:

$z''_{xy}(x,y)\neq z'_y(x,y)$ .

See Second-order partial derivatives.

Antwoord 4 feedback

Wrong: Do not forget the chain rule.

See Chain rule.