Question

(b). Use the chain rule to find me and where w = 22 + y2 + 22, x = st, y = scost, z = ssint when s = 1 and t = 0.

Answer 1

a=st, =s cost Then by Jo ax 2x Os aw ay os + az as (b) Here w=x²74²7 22 y = z = ssint clearly w is a function of x,y,z and x, y, z each of functions of sandt chain rule, we get ow Do dz ay as (2x). (t) + (24). (cost)+(22). (Sint) = 2 [nt + y cost + z sint When sal and t=0, we get x = 0, y = 1, 2 = 0 ---- (2) When s=1 and t=0, [ by (1) and (2)] Again, ow aw dz gw ax att by az at (2x)=(s) +(2p).Es.&int) + (22). (s 005 t) 2 [as-yssint + zs cost] --- (3) 2 os aw ax ou ou + Ot

From (2) and (3) we get When s=1 and t=0 aw at Herrice, When s=1 When s=1 and t=0, = 2 and os Jw st