Exercise 5 | Wiskunde op Tilburg University

Determine the derivative of

$y(x)=\dfrac{2^x+1}{\frac{1}{2}x^2+x+1}$ in

$x=0$ .

Antwoord 1 correct

Correct

Antwoord 2 correct

Fout

Antwoord 3 optie

2

Antwoord 3 correct

Fout

Antwoord 4 optie

$-1$

Antwoord 4 correct

Fout

Antwoord 1 optie

$\ln(2)-2$

Antwoord 1 feedback

Correct:

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

Hence,

$y'(0)=\dfrac{1\ln(2)1-2\cdot1}{1^2}=\ln(2)-2$ .

Go on.

Antwoord 2 feedback

Wrong:

$y'(0) \neq 0$ .

Try again.

Antwoord 3 feedback

Wrong: The question is not to determine

$y(0)$ .

Try again.

Antwoord 4 feedback

Wrong:

$2^0 \neq 0$ and the derivative of

$2^x$ is not equal to