Exercise 3 | Wiskunde op Tilburg University

Determine the derivative of

$f(x)=\dfrac{x+2}{2^x}$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

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

Antwoord 2 correct

Fout

Antwoord 3 optie

$f'(x)=\dfrac{x+3}{2^x}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$f'(x)=\dfrac{(x+3)\ln(2)}{2^x}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$f'(x)=\dfrac{1-(x+2)\ln (2)}{2^x}$

Antwoord 1 feedback

Correct:

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

Go on.

Antwoord 2 feedback

Wrong: The derivative of

$2^x$ is not

Antwoord 3 feedback

Wrong: The quotient rule does not state the following.

Let

$y(x) = \dfrac{u(x)}{v(x)}$ . Then:

$y'(x) = \dfrac{u'(x)v(x) + u(x)v'(x)}{\big(v(x)\big)^2}.$

See Quotient rule (film).

Antwoord 4 feedback

Wrong: The quotient rule does not state the following.

Let

$y(x) = \dfrac{u(x)}{v(x)}$ . Then:

$y'(x) = \dfrac{u'(x)v(x) + u(x)v'(x)}{\big(v(x)\big)^2}.$

See Quotient rule (film).