Question

use the chain rule to find dz/ds and dz/dt. z=arcsin(x-y), x=s^2+t^2, y=2-6st. dz/ds=? dz/dt=?

Answer 1

Soultion given that 2= arcsin (x-4) sin (2-Y), X= 32+ + 2 and Y = 2-65+ うNow 28 put am at 50 d2 at dz. dx + d2 dy dst at dy at Hele = 2 o sint(2-4) $²++² - +59-6=h SO ī XP louro = d2 dac = of 11-06-12 dt ZP - 59 - dy and dy at | 1-(8-4)2 so dz d# Cat) J 1-(x-4)2 (65) 11-(3-y)2 d2 +65) at Now d2 Jl-(x+y)2 (++65) | 1-(82++2_8+68+)2 ملح

dz dt 9+ +63 ST-((S++) d2 dt SHOP 24.63)2 (2++65) |-(s2++2_2+68+)2 Are. = Now we ZP pult ds 50 = d2 ds d2 dx dx SÞ + d2 dy dy ds Hele - dz dx 11- (x4) ZP pub (x-4)2 dy 1-(7-4)2 dx = as and dy 2+ ds SP uaut = ZP (-2+) (as) 1-(x-4)2 ds - 1 51-(x-4)² dz ds Locy (25++) 11-08-42 9S++) 11-182442-4+68+)2 so = dz ds Ar.