SOLUTION: Hello good friends . I have an implicit differentiation question if someone could please be kind enough to help me out . implicitly differentiate , ycos(1/y)=4x+4y they are asking

Question 958977: Hello good friends . I have an implicit differentiation question if someone could please be kind enough to help me out . implicitly differentiate , ycos(1/y)=4x+4y they are asking for dy/dx thank you! this is a tough one ! At least for me : )
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(1/y)=4x+4y
----
Rewrite::
y^-1 = 4x + 4y
----
Differentiate::
-y^-2*y' = 4 + 4y'
----
solve for y'
6y' = -y^-2 - 4
----
y' = (-1/6)((1/y^2)+4)
==================
Cheers,
Stan H.
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Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Step by step.
It's not tough, but it's easy to make a mistake.
Left side, you have a product.
So the derivative a product is,

So left hand side is,

Use the chain rule for the first derivative,

Putting it all together,

Now the right hand side is straight forward,

So then,

Re-arranging,

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