Consider the function
$$z(x,y) = \ln(2x + 3) + 3xy^4 + e^{y}.$$
Determine $z'_x(x,y)$.
$$z(x,y) = \ln(2x + 3) + 3xy^4 + e^{y}.$$
Determine $z'_x(x,y)$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$z'_x(x,y) = 12xy^3 + e^{y}.$
Antwoord 2 correct
Fout
Antwoord 3 optie
$z'_x(x,y) = \dfrac{2}{2x+3} + 12y^3 + e^{y}.$
Antwoord 3 correct
Fout
Antwoord 4 optie
$z'_x(x,y) = \dfrac{2}{2x+3} + 3y^4 + 12xy^3 + e^{y}.$
Antwoord 4 correct
Fout
Antwoord 1 optie
$z'_x(x,y) = \dfrac{2}{2x+3} + 3y^4.$
Antwoord 1 feedback
Correct: We have to determine the partial derivative with respect to $x$. Hence, we can consider $y$, and also $y^4$ and $e^y$, as constants. The partial derivative of $z(x,y)$ with respect to $x$ is:
$$z'_x(x,y) = \dfrac{1}{2x+3} \cdot 2 + 3y^4 \cdot 1 + 0 = \dfrac{2}{2x+3} + 3y^4.$$
Here we use the sum rule, the scalar product rule and the chain rule.
Go on.
$$z'_x(x,y) = \dfrac{1}{2x+3} \cdot 2 + 3y^4 \cdot 1 + 0 = \dfrac{2}{2x+3} + 3y^4.$$
Here we use the sum rule, the scalar product rule and the chain rule.
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 Exanple 3.
See Partial derivatives, Example 1, Example 2 and Exanple 3.
Antwoord 3 feedback
Wrong: With respect to which variable should $z(x,y)$ be differentiated?
See Partial derivatives, Example 1, Example 2 and Exanple 3.
See Partial derivatives, Example 1, Example 2 and Exanple 3.
Antwoord 4 feedback
Wrong: With respect to which variable should $z(x,y)$ be differentiated?
See Partial derivatives, Example 1, Example 2 and Exanple 3.
See Partial derivatives, Example 1, Example 2 and Exanple 3.