Implicit Differentiation problem

[DazedandConfuzed]

Ok heres the problem:


Use implicit differentiation to find dy/dx

4y^2 = (3x-2)/(3x+2)

(8y)(dy/dx) = d/dx ((3x-2)/(3x+2))

for d/dx((3x-2)/(3x+2))

((3x+2)d/dx(3x-2) - (3x-2)d/dx(3x+2))/((3x+2)^2)

(3(3x+2) - 3(3x-2))/((3x+2)^2)

12/((3x+2)^2)

Now the problem looks like this..

(8y)(dy/dx) = (12/((3x+2)^2))

and here is where the confusion starts.

dy/dx = 3/(2y(3x+2)^2)

how did bringing the 8y to the other side change the numerator from 12 to 3? How was the denominator changed?

 

[wjm11]

Use implicit differentiation to find dy/dx

4y^2 = (3x-2)/(3x+2)

(8y)(dy/dx) = d/dx ((3x-2)/(3x+2))

for d/dx((3x-2)/(3x+2))

((3x+2)d/dx(3x-2) - (3x-2)d/dx(3x+2))/((3x+2)^2)

(3(3x+2) - 3(3x-2))/((3x+2)^2)

12/((3x+2)^2)

Now the problem looks like this..

(8y)(dy/dx) = (12/((3x+2)^2))

and here is where the confusion starts.

dy/dx = 3/(2y(3x+2)^2)

how did bringing the 8y to the other side change the numerator from 12 to 3? How was the denominator changed?

Just simple algebra (dividing both sides by 8y) and simplification: 12/(8y) = 3/(2y)