Implicit differentiation find dy/dx and d2y/dx2

[mattmannmf]

2xy=3x-y^2

find dy/dx and d2y/dx2

I just want to make sure my answer is right and simplified

I got dy/dx= (3-2y)/ (2x+2y)

Now d2y/dx2 took some time but this is what i got:

(-12x+2x2y+9+4yx-14y-4y^2) / ((x+y)(2x+2y)^2)

 

[n!kofeyn]

Your dy/dx is correct. I didn't work out the second derivative, but as long as you took the derivative of dy/dx using the quotient rule and implicit differentiation, replacing dy/dx in that expression with what you found, and then simplifying correctly, then you did it right.

 

[mattmannmf]

yeah, i did that must i just wasn't to sure with my algebra (thats usually the step i would mess up). thanks though!

 

[blake knight]

I don't know if you can reduce this to a more simpler form but this is simplest i got: y"=(3-2y)(3+8x+6y)/8(x+y)^3

 

[mattmannmf]

was this from the equation i have up there or did u do this from the beginning of the problem?

 

[blake knight]

the answer is yes and yes.