Find the Gradient Vector Field of the Function $f ( x , y ) = \ln \left( \sqrt { x ^ { 2 } + y ^ { 2 } } \right)$

question 100

Multiple Choice

Find the gradient vector field of the function $f ( x , y ) = \ln \left( \sqrt { x ^ { 2 } + y ^ { 2 } } \right)$ .

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

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