Question

Question 7 * Use implicit differentiation to find of the following curve at the point (1, 29). y= x + sin xy b- Show that as, is zero in two differentiation steps only f(x,y) = xey?/« axay - Show that ox ay is zero in three differentiation steps only. f(x,y) = y² + y(sin x - **). z = -1 Question 8 Let w = z - sin(xy) where x = at y = ln(t) Find dw/dt by:- 4. Using Chain Rule principles b- Expressing (w) in term of (t) then differentiating directly a=51

Answer 1

Q© page-1 @ Ans! Step-1 Given y? x²+ sinsy to find dy at point Arian) doc? Step-2 differenticete both sidesworot x. slt sin(xy)) doc aydy dac = 206+ los cocy) de czy- X C«f(y)) = 2c + y los (33) dy dxca axty cof(xy) ay-glosary) A Step 3 Differentiate ean ( @wirt x. dy. (2y_tescos) lef2c43606x5)-(206+y cosces) ec29-X68x3) daca d (2y - 32608964)2

So, now page-2 dy. -2y=sinbey)-zey sin(y)+qy ty608438) Czy-2 C08C044) daca Bainile mi?)-2ftif2t Sincept + 4624) doc? Now find value cet point (Tiat) CTT 2005 -2(27) +21 (os (22) ( 21217) - (11) 68 (272) 87-20173 sin(7²) + 2 608² (272) (4TT-TT 60% cob (242733 -C71,2m) = -4.0507 dx? (6) Ans! Step-1 85f Show that is zero in two do?ay3 diffeocrticel Step., ffxy) - aces scegli

Step-2 page-3 & c. (c) =) •(1) First, find locat pe care 12 love being Novo مه 2 doc? doc (xceed 7) 2 (34) (ocella) yo } 0. doc? It zero in tivo diff. Step. Horice proved. Ansi Step-1 18 zon in three Show that J5 f dich yß diffcrention fteps. floco)= y + y (simx-24)

page-4 First find d doc gitg (-3c4+ sin() g (42) + d doc (y (-x+ +8 in (30) dx =) ya dx Novo, 9) Otello (2456) (-3c4+8inco 3) 4( 42 +608(20) Per la ty (20 2.3inco). o 13-06-22 sati ) -> sely(-432 +60860) =) -4(1280+ sina (77% (-*** **nm)+4 [-284 sincs) a) da (+4(1222 +sin(27) = -106² Sirl (22) Abco, d3 dicedy How,

page-5 Now, jt (g?ty(+24+ 8in(20) dx?ty? (4746-**+ 80 609) + d 3 d gy (-122?- sino) The derivative of constant iso soi d I (-1222 sinc:)) = 0 St Show 2000, Hence provede
NOTE:-As I see here different multiple type question asked but as per our policy we can solve only one different multiple type question.so I solve Question no (7) all subparts if you want solution of left question post again definitely we help you. Thnks