Find All the Second Order Partial Derivatives of the Given $f ( x , y ) = x ^ { 2 } + y - e ^ { x + y }$

question 129

Multiple Choice

Find all the second order partial derivatives of the given function.
- $f ( x , y ) = x ^ { 2 } + y - e ^ { x + y }$

• A) \(\frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { x } ^ { 2 } } = 2 - \mathrm { y } ^ { 2 } \mathrm { e } ^ { \mathrm { x } + y } ; \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { y } ^ { 2 } } = - \mathrm { x } ^ { 2 } \mathrm { e } ^ { \mathrm { x } + y } ; \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { y } \partial \mathrm { x } } = \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { x } \partial \mathrm { y } } = - \mathrm { y } ^ { 2 } \mathrm { e } ^ { \mathrm { x } + \mathrm { y } }\)
• B) \(\frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { x } ^ { 2 } } = 2 + \mathrm { e } ^ { \mathrm { x } + \mathrm { y } } ; \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { y } ^ { 2 } } = \mathrm { e } ^ { \mathrm { x } + \mathrm { y } } ; \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { y } \partial \mathrm { x } } = \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { x } \partial \mathrm { y } } = \mathrm { e } ^ { \mathrm { x } + \mathrm { y } }\)
• C) \(\frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { x } ^ { 2 } } = 2 - \mathrm { e } ^ { \mathrm { x } + \mathrm { y } } ; \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { y } ^ { 2 } } = - \mathrm { e } ^ { \mathrm { x } + \mathrm { y } } ; \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { y } \partial \mathrm { x } } = \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { x } \partial \mathrm { y } } = - \mathrm { e } ^ { \mathrm { x } + \mathrm { y } }\)
• D) \(\frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { x } ^ { 2 } } = 1 - \mathrm { e } ^ { \mathrm { x } + \mathrm { y } } ; \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { y } ^ { 2 } } = - \mathrm { e } ^ { \mathrm { x } + \mathrm { y } } ; \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { y } \partial \mathrm { x } } = \frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { x } \partial \mathrm { y } } = - \mathrm { e } ^ { \mathrm { x } + \mathrm { y } }\)

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