Hi there. it would be greatly appreciated if the following calculus and vectors (university level) homework questions are solved with full solutions. I am lost on how to solve them as I'm trying to catch up on the course. Thank you,

Find the gradient vector field of the funchien f ( n, 4 ) = = x cos(y ) + sinly) ( Please Show All your Work. ) Ophen 4 : F ( 7 , y ) = - cusly)i+ (nsin (y ) + coscgg> > i Option 2 : F (n, 9) = - cos (y) i + 07 Opticn 3 : F ( 2 , y ) = - sinly ) i - 2 - cos(y) ] Option 4: F ( n , y ) = - ncos (y)i - sincy); Find the divergence of F for vector field F ( n , y , z ) = ( y z - n2 ) ( n + y) ; + ( zz - x2) (y + z)j + (x2 - yz > z- x)k ( Please Show All your Work. )3 Find the work done by force F ( a,y ) = - 49 1 - 2 2 j + ( x + g j k in moving an object along the curve r(t ) = costi + sintj + 1% 4 Where Oct 271. ( Please Show All your Work