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Let Be a Differential K-Form, Be a Differential

Question 7

Multiple Choice

Let Let be a differential k-form, be a differential l-form, and be an m-form on a domain D . Find an expression for a product rule for the exterior derivative of the wedge product . A) d( ) = (d ) + d( ) + d( ) B) d( ) = (d ) (d ) (d ) C) d( ) = (d ) + d( ) + d( ) D) d( ) = (d ) + d( ) + d( ) E) d( ) = (d ) + d( ) + d( ) be a differential k-form, Let be a differential k-form, be a differential l-form, and be an m-form on a domain D . Find an expression for a product rule for the exterior derivative of the wedge product . A) d( ) = (d ) + d( ) + d( ) B) d( ) = (d ) (d ) (d ) C) d( ) = (d ) + d( ) + d( ) D) d( ) = (d ) + d( ) + d( ) E) d( ) = (d ) + d( ) + d( ) be a differential l-form, and Let be a differential k-form, be a differential l-form, and be an m-form on a domain D . Find an expression for a product rule for the exterior derivative of the wedge product . A) d( ) = (d ) + d( ) + d( ) B) d( ) = (d ) (d ) (d ) C) d( ) = (d ) + d( ) + d( ) D) d( ) = (d ) + d( ) + d( ) E) d( ) = (d ) + d( ) + d( ) be an m-form on a domain D Let be a differential k-form, be a differential l-form, and be an m-form on a domain D . Find an expression for a product rule for the exterior derivative of the wedge product . A) d( ) = (d ) + d( ) + d( ) B) d( ) = (d ) (d ) (d ) C) d( ) = (d ) + d( ) + d( ) D) d( ) = (d ) + d( ) + d( ) E) d( ) = (d ) + d( ) + d( ) Let be a differential k-form, be a differential l-form, and be an m-form on a domain D . Find an expression for a product rule for the exterior derivative of the wedge product . A) d( ) = (d ) + d( ) + d( ) B) d( ) = (d ) (d ) (d ) C) d( ) = (d ) + d( ) + d( ) D) d( ) = (d ) + d( ) + d( ) E) d( ) = (d ) + d( ) + d( ) . Find an expression for a product rule for the exterior derivative of the wedge product 11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 .


A) d(11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 ) = (d11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 ) 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 + 11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 d(11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 ) 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 + 11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_1111ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 d(11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 )
B) d(11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 ) = (d11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 ) 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 (d11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 ) 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 (d11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 )
C) d(11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 ) = 11ee77e1_778f_707a_a0f8_0f0cf020c8ae_TB9661_11 (d11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 ) 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 + 11ee77e1_778f_707b_a0f8_b330ac7d8ff2_TB9661_11 11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 d(11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 ) 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 + 11ee77e1_778f_707c_a0f8_3fc788d7350d_TB9661_11 11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 d( 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 )
D) d(11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 ) = (d11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 ) 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 + 11ee77e1_778f_707d_a0f8_a543d7ec6294_TB9661_11 11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 d(11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 ) 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 + 11ee77e1_778f_707e_a0f8_0d7d97689662_TB9661_11 11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 d(11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 )
E) d(11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 ) = (d11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 ) 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 + 11ee77e1_778f_978f_a0f8_bb7a8348f6a4_TB9661_11 11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 d(11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 ) 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 + 11ee77e1_778f_9790_a0f8_8192a9a2493f_TB9661_11 11ee7bc3_71c2_6b7a_ae82_2ff308d77e4f_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 11ee7bc3_ff64_cfeb_ae82_d9001ab9380d_TB9661_11 11ee7bc5_64fc_b24d_ae82_a1e274b00064_TB9661_11 d(11ee7bc4_a745_09fc_ae82_03df54d144ea_TB9661_11 )

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