Find y'' by implicit differentiation. x^2 + 6y^2 = 6

Question

Please help me

Answer 1

Implicit differentiation means to derive both sides of the equation using the chain rule.

 

(x² + 6y²)' = 6'

 

2x + 12yy' = 0

 

 

Subtract 2x on both sides of the equation.

 

12yy' = -6x

 

 

Divide both sides of the equation by 12y.

 

y' = 6x / 12y

 

y' = (1/2)x/y

 

 

Now we take the derivative of y' to get y'' (not sure if you are looking for y'', unless there is a minor typo in your question).  We can write y' so that we don't have a denominator.

 

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

 

 

y'' = (1/2)[y^-1 - xy^-2y']

 

y'' = (1/2y) - (x /2y²)y^'