# Math Help - Implicit differentiation!

1. ## Implicit differentiation!

Hi all
I am trying to solve the following problem and my answer does not match up with that in the book.I have done it 4 times and have got it wrong each time.
Can somebody do it before it drives me mad.

Find dy/dx as a function of x and y for y=x-y+2y^3-3Lnx

differentiate both sides;

dy/dx= 1-(dy/dx)+6y^2.(dy/dx)-3x^-1

2dy/dx-6y^2.(dy/dx)=1-3x^-1

dy/dx(2-6y^2)=1-3x^-1

dy/dx=(1-3x^-1)/ (2-6y^2)

The answer in my book is dy/dx=(x-3)/[3x(1+2y^2)]

I have followed the examples in the book fine, -this one is driving me mad.

Help appreciated
John

2. ## Re: Implicit differentiation!

Originally Posted by celtic1234
Hi all
I am trying to solve the following problem and my answer does not match up with that in the book.I have done it 4 times and have got it wrong each time.
Can somebody do it before it drives me mad.

Find dy/dx as a function of x and y for y=x-y+2y^3-3Lnx

differentiate both sides;

dy/dx= 1-(dy/dx)+6y^2.(dy/dx)-3x^-1

2dy/dx-6y^2.(dy/dx)=1-3x^-1

dy/dx(2-6y^2)=1-3x^-1

dy/dx=(1-3x^-1)/ (2-6y^2)

The answer in my book is dy/dx=(x-3)/[3x(1+2y^2)]

I have followed the examples in the book fine, -this one is driving me mad.

Help appreciated
John
I get $\frac{dy}{dx} = \frac{x - 3}{2x(1 - 3y^2)}$, which is consistent with your answer. So either the answer in the book is wrong or there is a typo in the original question.

3. ## Re: Implicit differentiation!

thank you,
It is basic enough which was the reason it bothered me that i could not get it correct.
Anyone else think it's a typo?
thanks again
John