2.5

3) x^(1/2)+y^(1/2)=9 (1/2)x^(-1/2)+(1/2)y^(1/2)y'=0 y'=-x^(1/2)/y^(1/2) y'= -(x/y)^(1/2) worked by Layne Miller Checked by Abby Newton

4) x^3+y^3=8 3x^2+3y(dy/dx)= 0 3y (dy/dx)= -3x^2 [3y (dy/dx)/ 3y)= (-3x^2)/3y^2 dy/dx= -x^2/y^2 worked by Hyun Bang Correct! Checked by Audrey Luecken 8.) sq.rt.(xy)=x-2y (xy)^(1/2)= x-2y 1/2(xy)^-(1/2)=1-2 1/2(xy)^-(1/2)(dy/dx)=-3 dy/dx(1/2*(xy)^-(1/2))=-3 dy/dx=-3/(1/2)(xy)^(-1/2) Worked by Abby Newton checked correct by layne miller

 9) y'=3x^2-(6x(y)+3x^2(dy/dx))+ 2(2y(dy/dx))+2x(y^2)=12 =-3x^2-6xy+3x^2(dy/dx)+4y(dy/dx)+2xy^2=12 3x^2(dy/dx)+4y(dy/dx)=12+3x^2+6xy-2xy^2 (dy/dx)=(12+3x^2+6xy-2xy^2)/(12xy) Worked by Nadia Guillen-- I worked this problem at 7:57pm oct.12 but it got deleted... correct. checked by Hyun Bang

10. 2sinxcosy=1 (2cosx)(-siny dy/dx)=0 dy/dx(-siny)=-2cosx dy/dx=-2cosx/-siny dy/dx=2cosx/siny worked by emily othold correct checked by sunny krishnan

11) cosx-4(sin2y)y'= 0 y'= (cosx)/(4sinx2y) Worked by Michelle Tassin Correct! Checked by Rachel Pearce

14.) cot y = x-y -sin dx/dy = 1- dx/dy 2( -sin dx/dy) = 1 -sin dx/dy= 1/2 dx/dy = 1/ -sin2

Worked by ??? Correct! Checked by Krissy Denby

15) y=sin(xy) y dx/dy = cos(xy) dx/dy dx/dy=[y cos(xy)]/[1-xcos(xy)] worked by Alex Stevens Checked by Thomas Sturm

25. x^2/3+y^2/3= 5, (8,1) 2/3x^-1/3+2/3y^-1/3y=o yprime=-x^1/3/(y^-1/3) =-cubed root of y/x at (8,1) y prime= -1/2 worked byh sheridan gabrisch checked byellen wagner Worked by Warner Boin correct checked by will mccrocklin

35. WORKED BY ERIN RANDALL xy=1 (1,1) xy'+y=0 y'= -y/x At (1,1): y'= -1 Tangent Line: y-1=-1(x-1) y=-x+2 Correct! checked by Morgan Clinkscales

49. y^2=x^3 dy/dx=3x/3y d^2y/dx^2=2y(3) - [(3x)(2dx/dy)]/4y^2 =6y-[6x(2x/y)]/4y^2 =(3y-6x^2)/2y^2 worked by Kara Manning Checked by Kendall Jones

53. Worked by Hayley Linton checked by Nolan Blair