Solve the problem.
-$$\text { Evaluate } \frac { \partial \mathrm { w } } { \partial \mathrm { u } } \text { at } ( \mathrm { u } , \mathrm { v } ) = ( 4,2 ) \text { for the function } \mathrm { w } = \mathrm { xz } + \mathrm { yz } - \mathrm { z } ^ { 2 } ; \mathrm { x } = \mathrm { uv } , \mathrm { y } = \mathrm { uv } , \mathrm { z } = \mathrm { u }$$
A) 0
B) 24
C) -8
D) 32

Question

Quizplus · Accepted Answer

First, substitute $x = uv$, $y = uv$, and $z = u$ into $w = xz + yz - z^2$ to get $w = u^2v + u^2v - u^2$. Simplify to $w = 2u^2v - u^2$. Then, differentiate $w$ with respect to $u$ to get $\frac{\partial w}{\partial u} = 4uv - 2u$. Substituting $u = 4$ and $v = 2$ gives $\frac{\partial w}{\partial u} = 4(4)(2) - 2(4) = 32 - 8 = 24$.

Solve the Problem A) 0 B) 24 C) -8 D) 32

Solve the Problem A) 0
B) 24
C) -8
D) 32