How to Use Implicit Differentiation to Solve for y' in xy^1/2 = 1 + x^2y

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SUMMARY

The discussion focuses on using implicit differentiation to solve for y' in the equation xy^(1/2) = 1 + x^2y. The user correctly differentiates the right-hand side but struggles with isolating y' on the left-hand side. The correct differentiation leads to the expression ((1/2xy)^(-1/2))y + y'x = 2xy + x^2y'. The key takeaway is the importance of accurately applying the product and chain rules in implicit differentiation.

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ms. confused
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How do I correctly differentiate this using implicit differentiation:

xy^1/2 = 1 + x^2y

I got to here before I started wondering how I would properly isolate y':

((1/2xy)^-1/2)y + y'x = 2xy + x^2y'

How far off the beaten path am I on this?
 
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The right hand side of your equation looks OK. Redo the left side.
 

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