Find the Divergence of the Vector Field $\overrightarrow { \mathbf { F } } ( x , y , z ) = 10 x ^ { 6 } \hat { \mathbf { i } } - x y ^ { 5 } \hat { \mathbf { j } }$

question 108

Multiple Choice

Find the divergence of the vector field. $\overrightarrow { \mathbf { F } } ( x , y , z ) = 10 x ^ { 6 } \hat { \mathbf { i } } - x y ^ { 5 } \hat { \mathbf { j } }$

• A) \(\operatorname { div } \overrightarrow { \mathrm { F } } ( x , y , z ) = 60 x ^ { 7 } - 6 x y ^ { 6 }\)
• B) \(\quad \operatorname { div } \overrightarrow { \mathrm { F } } ( x , y , z ) = 60 x ^ { 5 } - 5 x y ^ { 4 }\)
• C) \(\operatorname { div } \overrightarrow { \mathrm { F } } ( x , y , z ) = 10 x ^ { 6 } \hat { \mathbf { i } } - 6 x y ^ { 5 } \hat { \mathbf { j } }\)
• D)\(\operatorname { div } \overrightarrow { \mathrm { F } } ( x , y , z ) = \frac { 10 } { 7 } x ^ { 7 } - \frac { 1 } { 6 } x y ^ { 6 }\)
• E)\(\operatorname { div } \overrightarrow { \mathrm { F } } ( x , y , z ) = \frac { 10 } { 7 } x ^ { 7 } \hat { \mathbf { i } } - \frac { 1 } { 5 } x y ^ { 4 } \hat { \mathbf { j } }\)

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