Use implicit differentiation to find dy/dx and d^2y/dx^2

6sqrt(y)=x-y

I've used two variations of this equation and I can't figure out how to solve for dy/dx after bringing all of the variables to one side. (Part A of the question on the left side of my page)

I get to dy/dx (3/sqrt(y)+1)=1 and cannot understand how the solution is sqrt(y)/sqrt(y)+3. What am I missing?

Thank you in advance,

Doc Feb 02, 2022, 10.56(1)-01.pdf - Adobe Acrobat Reader DC (64-bit) X File Edit View Sign Window Help Home Tools Doc Feb 02, 2022, ... X ? Sign In T 1 / 1 X Search 'Reduce Size' Export PDF dy AND dy Edit PDF d x d x 2 dx xy+ 3 6 4 = X - y = NY+3 #x - 5/ 8x NY + 3 Create PDF ( 5 + 3 ) 2 x ( by / 2 ) = 1x X - day Comment = NY+ 3 : 1 du - NY FOX 3//2. 80 = 1 - 94 ( 7+ 3 ) Combine Files 3 SUBSTITUTE hy EDOrganize Pages ~ 3 dy + dy = 1 - NY - 2,54 NY + 3 Ny dx d (Ny + 3 ) 2 Delete, insert, extract and rotate pages. dy ( NY + 1 ) = 1 L-NY dx 2 2 5#1 3 . 2,NY+ 3 (y+ 3)2 . 217 +3 Try now dy = HOW IS THIS dx SIMPLIFIED ? ? 2 17+3 _ Ny . 287+3 Compress PDF dy = Ny 2 2 .17 + 3 dx Ny + 3 (y + 3 ) . 251 13 Redact ry + 3 - Ny Protect 2457 +3) =) Addnha Cian 2 ( 54+3 ) Convert, edit and e-sign PDF forms & agreements Free 7-Day Trial E 11:05 AM 2/2/2022 1