Let $f ( x , y ) = \frac { x } { y } + \frac { y } { x }$

question 160

Multiple Choice

Let $f ( x , y ) = \frac { x } { y } + \frac { y } { x }$ . Find the gradient vector $\nabla f$ .

• A) \(2 x \mathbf { i } + 2 y \mathbf { j }\)
• B) \(2 y \mathbf { i } + 2 x \mathbf { j }\)
• C) \(- \frac { y } { x ^ { 2 } } \mathbf { i } - \frac { x } { y ^ { 2 } } \mathbf { j }\)
• D) \(\frac { 1 } { y } \mathbf { i } + \frac { 1 } { x } \mathbf { j }\)
• E) \(x \mathbf { i } + y \mathbf { j }\)
• F) \(y \mathbf { i } + x \mathbf { j }\)
• G) \(\frac { y } { x ^ { 2 } } \mathbf { i } + \frac { x } { y ^ { 2 } } \mathbf { j }\)
• H) \(\left( \frac { 1 } { y } - \frac { y } { x ^ { 2 } } \right) \mathbf { i } + \left( \frac { 1 } { x } - \frac { x } { y ^ { 2 } } \right) \mathbf { j }\)

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