Determine the derivative of $y(x) = 37 \cdot 2^x$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$y'(x) = 37\cdot 2^x$.
Antwoord 2 correct
Fout
Antwoord 3 optie
$y'(x) = 37x2^{x-1}$.
Antwoord 3 correct
Fout
Antwoord 4 optie
$y'(x) = \ln(2)\cdot 2^x$.
Antwoord 4 correct
Fout
Antwoord 1 optie
$y'(x) = 37\cdot \ln(2) 2^x$.
Antwoord 1 feedback
Correct: We use the scalar product rule with $c=37$ and $u(x) = 2^x$. In two steps we find $y'(x)$ (possibly see Derivatives of elementary functions):
$$\begin{align*}
u'(x) &= 2^x \ln(2) = \ln(2)2^x,\\
y'(x) &= 37 \cdot \ln(2)2^x.
\end{align*}$$
Go on.
$$\begin{align*}
u'(x) &= 2^x \ln(2) = \ln(2)2^x,\\
y'(x) &= 37 \cdot \ln(2)2^x.
\end{align*}$$
Go on.
Antwoord 2 feedback
Wrong: You did use the scalar product rule, but the derivative of $2^x$ is incorrect.
See Derivatives of elementary functions.
See Derivatives of elementary functions.
Antwoord 3 feedback
Wrong: You did use the scalar product rule, but the derivative of $2^x$ is incorrect.
See Derivatives of elementary functions.
See Derivatives of elementary functions.
Antwoord 4 feedback