Find the first partial derivative for the function $f ( x , y , z ) = 5 x ^ { 2 } y - 3 x y z + 6 y z ^ { 2 } \text { with }$ respect to z.
A) $f _ { z } ( x , y , z ) = - 3 x z + 9 y z$
B) $f _ { z } ( x , y , z ) = - 6 x y + 12 y z$
C) $f _ { z } ( x , y , z ) = 12 x y + 15 y z$
D) $f _ { z } ( x , y , z ) = 3 x z + 12 y z$
E) $f _ { z } ( x , y , z ) = - 3 x y + 12 y z$

Question

Find the first partial derivative for the function $f ( x , y , z ) = 5 x ^ { 2 } y - 3 x y z + 6 y z ^ { 2 } \text { with }$ respect to z. 
A) $f _ { z } ( x , y , z ) = - 3 x z + 9 y z$
B) $f _ { z } ( x , y , z ) = - 6 x y + 12 y z$
C) $f _ { z } ( x , y , z ) = 12 x y + 15 y z$
D) $f _ { z } ( x , y , z ) = 3 x z + 12 y z$
E) $f _ { z } ( x , y , z ) = - 3 x y + 12 y z$

Quizplus · Accepted Answer

The partial derivative of $f(x, y, z)$ with respect to $z$ is found by differentiating each term of the function with respect to $z$, treating $x$ and $y$ as constants. The derivative is $-3xy + 12yz$.

Find the First Partial Derivative for the Function f(x,y,z)=5x2y−3xyz+6yz2 with f ( x , y , z ) = 5 x ^ { 2 } y - 3 x y z + 6 y z ^ { 2 } \text { with }f(x,y,z)=5x2y−3xyz+6yz2 with

Find the First Partial Derivative for the Function $f ( x , y , z ) = 5 x ^ { 2 } y - 3 x y z + 6 y z ^ { 2 } \text { with }$