use implicit differentiation to find y'

Question

x+2y=sqrt(y)

Answer 1

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Answer 2

x + 2y = y^1/2

 

You will differentiate both sides of the equation using the chain rule.

 

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

 

1 + 2y' = y' / (2√y)

 

 

Multiply both sides of the equation by 2√y.

 

2√y + 4y'√y = y'

 

 

Move all the y' terms to the left side of the equation.  Move all the other terms to the right side.

 

4y'√y - y' = 2√y

 

 

Factor out a y'.

 

y' (-1 + 4√y) = 2√y

 

 

Finally, divide both sides of the equation by the coefficient of y'.