Exercise 1 | Wiskunde op Tilburg University

$y(x)=\;^4\!\log 2x$ . Determine the second-order derivative

$y''(x)$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$y''(x)=\dfrac{1}{x \cdot \textrm{ln}(4)}$ .

Antwoord 2 correct

Fout

Antwoord 3 optie

$y''(x)=-\dfrac{1}{2x^2\cdot \textrm{ln}(4)}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$y''(x)=-\dfrac{1}{x^2}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$y''(x)=-\dfrac{1}{x^2\cdot \textrm{ln}(4)}$

Antwoord 1 feedback

Correct:

$y'(x)=\dfrac{1}{2x\textrm{ln}(4)}\cdot 2= \dfrac{1}{x \textrm{ln}(4)}=\dfrac{1}{\textrm{ln}(4)}\cdot x^{-1}$ ,
and

$y''(x)=\dfrac{1}{\textrm{ln}(4)}\cdot -x^{-2}=-\dfrac{1}{x^2\cdot\textrm{ln}(4)}$ .

Go on.

Antwoord 2 feedback

Wrong: You have to determine the second-order derivative.

Try again.

Antwoord 3 feedback

Wrong:

$y'(x)\neq -\dfrac{1}{2x\cdot \textrm{ln}(4)}$ .

See Chain rule.

Antwoord 4 feedback

Wrong:

$y'(x)\neq \dfrac{1}{x}$ .

See Derivatives of elementary functions.