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.
Go on.
Antwoord 2 feedback
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).
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).
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).