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

question 85

Multiple Choice

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) \(f _ { z } ( x , y , z ) = - 3 x y + 12 y z\)

---

Definitions:

Occupational Health

A multidisciplinary field concerning the safety, health, and welfare of people at their workplace.

Physical Injuries

Damage to the body caused by external force, possibly leading to pain, dysfunction, or both.

Interpersonal Relationships

Interpersonal Relationships involve connections and interactions between individuals, encompassing various forms such as friendships, familial ties, and romantic partnerships.

Adolescents

Young people in the transitional stage of physical and psychological development from the onset of puberty to adulthood.