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) \(\frac { \partial f } { \partial x } = \frac { 2 } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\) , \(\frac { \partial f } { \partial y } = \frac { 2 } { \left( x + y + z ^ { 2 } \right) ^ { 2 } }\) , \(\frac { \partial f } { \partial z } = \frac { 4 z } { ( x + y + z ) ^ { 2 } }\)

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