Implicit differentiation of xcos(y) + ycos(x) = 1

[CACain]

:Implicit Differentiation Problem -- Check my work?:

Think I placed this in the wrong forum...

I've worked it -- can someone just check my work?

Problem:

xcosy+ycos=1

My work:

[x (d/x)cosy + cosy (d/dx)x] + [y (d/dx)cosx + cosx (d/dx)y] = (d/dx) 1

-xsiny (dy/dx) + cos y - ysinx + cos x (dy/dx) = 0

-xsiny (dy/dx) + cos y = ysinx - cosy

dy/dx = (ysinx - cosy)/(-xsiny + cos x)


Meanwhile, could someone help me with this one...

squareroot (xy) = 1+(x^2)y

 

[Mulder]

dy/dx = (ysinx - cosy)/(-xsiny + cos x)

this final answer is right.

The second one is probably easier, have a go at it at least and we'll check the answer again?

 

[CACain]

Well, the problem with that one is the idea that I can't even get the first step... the derivative of sqrt (xy)

 

[quark]

Square the equation.