Consider the function
$$z(x,y) = x^y.$$
Determine $z'_y(2,3)$.
$$z(x,y) = x^y.$$
Determine $z'_y(2,3)$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$z'_y(2,3) = 12.$
Antwoord 2 correct
Fout
Antwoord 3 optie
$z'_y(2,3) = 8\ln(3).$
Antwoord 3 correct
Fout
Antwoord 4 optie
$z'_y(2,3) = 9\ln(3).$
Antwoord 4 correct
Fout
Antwoord 1 optie
$z'_y(2,3) = 8\ln(2).$
Antwoord 1 feedback
Correct: We have to determine the partial derivative with respect to $y$, which means that we can consider $x$ as a constant. The partial derivative of $z(x,y)$ with respect to $y$ is:
$$z'_y(x,y) = x^y \cdot \ln(x) = \ln(x)x^y.$$
Finally, we plug $(x,y)=(2,3)$ in:
$$z'_y(2,3) = \ln(2)\cdot2^3 = 8\ln(2).$$
Go on.
$$z'_y(x,y) = x^y \cdot \ln(x) = \ln(x)x^y.$$
Finally, we plug $(x,y)=(2,3)$ in:
$$z'_y(2,3) = \ln(2)\cdot2^3 = 8\ln(2).$$
Go on.
Antwoord 2 feedback
Wrong: With respect to which variable should $z(x,y)$ be differentiated?
See Partial derivatives, Example 1, Example 2 and Example 3.
See Partial derivatives, Example 1, Example 2 and Example 3.
Antwoord 3 feedback
Wrong: What is the derivative of an exponential function?
See Derivatives elementary functions, Example 1, Example 2 and Example 3.
See Derivatives elementary functions, Example 1, Example 2 and Example 3.
Antwoord 4 feedback
Wrong: You probably plugged in the wrong values for $x$ and $y$.
Try again.
Try again.