Consider the function
$$z(x,y) = \big( 3y + 2x\big)^5.$$
Determine $z'_y(2,1)$.
$z'_y(2,1) = 36015.$
$z'_y(2,1) = 12005.$
$z'_y(2,1) = 24010.$
$z'_y(2,1) = 61440.$
Wrong: You probably plugged in wrong values for $x$ and $y$.
Try again.
Correct: We have to determine the partial derivative with respect to $y$. Hence, we can consider $x$ as a constant. Then the partial derivative of $z(x,y)$ with respect to $y$ is:
$$z'_y(x,y) = 5 \cdot \big(3y + 2x\big)^{5-1} \cdot (3 + 0) = 15\big(3y + 2x\big)^4.$$
Finally, we plug in $(x,y)=(2,1)$:
$$z'_y(2,1) = 15\big(3\cdot 1+2\cdot 2\big)^4 = 15 \cdot 7^4 = 36015.$$
Go on.
Wrong: Do not forget to apply the composite power rule.
See Extra explanation: special cases, Example 1, Example 2 and Example 3.
Wrong: With respect to which variabele should $z(x,y)$ be differentiated?
See Partial derivatives, Example 1, Example 2 and Example 3.