Calculate $\frac { \partial f } { \partial x }$ $\frac { \partial f } { \partial y }$

question 51

Multiple Choice

Calculate $\frac { \partial f } { \partial x }$ , $\frac { \partial f } { \partial y }$ , and $\frac { \partial f } { \partial z }$ when defined. $f ( x , y , z ) = - \frac { 2 } { x + y + z ^ { 2 } }$

• A) \(\frac { \partial f } { \partial x } = - \frac { 2 } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\) , \(\frac { \partial f } { \partial y } = - \frac { 2 } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\) , \(\frac { \partial f } { \partial z } = \frac { 2 } { 2 z \left( x + y + z ^ { 2 } \right) ^ { 2 } }\)
• B) \(\frac { \partial f } { \partial x } = \frac { 2 } { x + y + z ^ { 2 } }\) , \(\frac { \partial f } { \partial y } = \frac { 2 } { x + y + z ^ { 2 } }\) , \(\frac { \partial f } { \partial z } = \frac { 4 z } { x + y + z ^ { 2 } }\)
• C) \(\frac { \partial f } { \partial x } = \frac { 2 } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\) , \(\frac { \partial f } { \partial y } = \frac { 2 } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\) , \(\frac { \partial f } { \partial z } = \frac { 4 z } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\)
• D) \(\frac { \partial f } { \partial x } = \frac { 2 x } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\) , \(\frac { \partial f } { \partial y } = \frac { 2 y } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\) , \(\frac { \partial f } { \partial z } = \frac { 4 z } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\)
• E) \(\frac { \partial f } { \partial x } = \frac { 2 } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\) , \(\frac { \partial f } { \partial y } = \frac { 2 } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\) , \(\frac { \partial f } { \partial z } = \frac { 4 z } { ( x + y + z ) ^ { 2 } }\)

Understand the concept of triangulation in research methodology.

Comprehend the significance of normal distribution in statistical analysis.

Recognize ethical considerations in psychological research.

Understand the significance of open practices in research for transparency.