Implicit Differentatiation Help for Homework!

[cv2yanks13]

Hi I need some help figuring these out... I've done them out... but I'd like to check my answers before I hand them in to be graded.

Use implict differentiation to find dy/dx for
x+sin(2y)=xy^2

Use Implicit differentiation to find the slope fo the curve given by the equation shown below at the point (-2,1). Then find the equation of the tangent line to the curve at that point.
y^2-2x-4y-1=0

 

[cole92]

For the first part, I believe this is correct:

[attachment=0:3nc3ut6q]asd.jpg[/attachment:3nc3ut6q]

I think you can take it from there.

 

[BigGlenntheHeavy]

\(\displaystyle 1) \ x+sin(2y) \ = \ xy^{2}, \ 1+2y'cos(2y) \ = \ y^{2}+2xyy'\)

\(\displaystyle 2xyy'-2y'cos(2y) \ = \ 1-y^{2}, \ Hence \ y' \ = \ \frac{1-y^{2}}{2xy-2cos(2y)}\)

\(\displaystyle 2) \ y^{2}-4y-2x-1 \ = \ 0, \ 2yy'-4y'=2, \ y' \ = \ \frac{2}{2y-4} \ = \ \frac{1}{y-2}\)

\(\displaystyle When \ y \ = \ 1, \ m \ = \ -1, \ hence \ y \ = \ -x-1, \ see \ graph.\)

[attachment=0:3qjqqg2d]mno.jpg[/attachment:3qjqqg2d]