Question

Let z = 8x² + 16xy - 8y2 , where x(t,s) = cosh (2t) cos (6s) and y(t,s) = sinh (2t) sin (6s). (JUse the chain rule to compute of at (ts) = (4 in (2)ā) дz (ii) Use the Chain rule to compute de at (t.s) Exact values Required. No Radicals permitted. Use Only Integers Or Fully Reduced Fractions.

Answer 1

Given z = 0x?+1684 -- Oy' be (7,5) = cosh (24) 205(68) (1,) - ko 5 (21) . An (64) het (3) ) + (%)(%) Partially Differentiating 02 – 8 (23) + 160my en cos (ca) [ain h (28)] 2 22 = 16 (x)(1) – 8 679) leo y Eusen (6) cash (143)2 | (16x+16) con (64). sinh (243) + [(162-164) (acosh (24) din 6s]

ze he ze txe ze xel se he - - - 6 sin ( 4 ) cosb () 24 - 6 cos (64) до (24) (k-x) 91 - 20 д2 . 16 (x+y) (- 6 so (КА)) tosh (24) + 16 (2-) 6cos (48) әк - 12 см ді, һ (21) Г+2 , 11 - - 36 (1) в. «(Е) ли, h = (4+1) +34 ( 1 ) cos • () sub = [4 oz] Гра -33-3411 (1-1) д.

mnie Cheez tel 011- Cate] yox (17 Chrzeze [(evy #) 24 von (K) y Ch-x) ze + [ccewe #? a) yuso () , so Ch14 891):] (featJust In 2

X 1.06066 s [4 42, 4]: cosef* 102 ] cos 6 (7) 1x = 106066] ylt en 2, ) = sinh (2 (4- 402) sin 6 () jy =o) Sinne = -113-137(1.06066+0) az --119.9993 dt 1202 = -1207 van 33.941 [1-060607 22 --35.9999 ds 25