Question

6. [-12 Points] DETAILS SCALCET8 14.5.012. Use the Chain Rule to find Oz/os and Oz/t. z = tan(u/v), u = 6 + 9t, v = 9s - 6t дz as oz at Need Help? Read It Talk to a Tutor 7. [-13 Points] DETAILS SCALCET8 14.5.021. Use the Chain Rule to find the indicated partial derivatives. z = x4 + x2y, x = 5 + 2t - u, θz oz oz when s = 4, t = 3, u = 1 Os Ot' du y = stu; Oz = Oz at = дz ou = Need Help? Read It Watch It Talk to a Tutor 8. [-/1 Points) DETAILS SCALCET8 14.5.029. Use this equation to find dy/dx. 7 tan-+(x2y) = x + xy2 dx Need Help? Read It Watch It Talk to a Tutor

Answer 1

Given that z= tan (/) where U = 6 stat v=9s-et So z = tan 6 Seat lia as-6t əz as 2813t z (tan ys (as 35-36) let ua 9- asest 38-at. Apply the chain rub 3 (8C) - 2.(260). až g)

a tan (u))= sec²(u). วิน o secº (0) Bs lastsed) a sec², ast37 ast31 35-at ) ) as 35 at asest sec Casa ( 35 at -@3t) 5 (35-a2t) + ? (25+3+)(35at)) (35-t) 2 as since os ( 9/) - 5- (1.01).9-5.3 (9) seca ase3t ) ( 35-at (2 305)) -(ast3t) $ (35=&t) + (35-24) es-at)? ) (-(as+at) }(35-84) +2 (35-at) () O » sec² 2513t 35-at (35-2t) ) see" (Sad) (65-4- (251st) (361) - 3 (2+) sec² ce asest 35-at ) (65-46 (3-(0)) (@s+3+))) Thus as +32 2 (tan (23131 -13 35 2t ) 2 t sec² (35-at)? (35-87

as sect 23+3+ ) 95 -67 + (2343) (24) (35-at) 2 35-at Thus ə ot 23+37 (tan ( 25131 35-at )) 13 s sec² (35-24) ( 35-at