Need help using implicit differentiation on equation:

3xy^2 + y^3 = 8

x^2/16 + 3y^2/13 = 1

I just do not know how to start it at all :( I tried using product rule and it didn't work

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- February 25th 2009, 02:20 PMmathamatics112Implicit differentation
Need help using implicit differentiation on equation:

3xy^2 + y^3 = 8

x^2/16 + 3y^2/13 = 1

I just do not know how to start it at all :( I tried using product rule and it didn't work - February 25th 2009, 02:35 PMskeeter
- February 25th 2009, 02:39 PMAmanda H
Product rule does come into it with the first part of the equation but you need to apply the chain rule as well.

first of all when you differentiate y it should become

So applying the chain rule to you get:

you deal with in a similar way.

Applying all this with the product rule the whole function should become:

You now need to rearrange to get

Put the on the other side

Take out as a common factor

Then divide to leave on its own

Differentiating y can be confusing so I can try to go over it in more detail if you want. - February 25th 2009, 02:40 PMmathamatics112
3xy^2 + y^3 = 8

now product rule...

(3)(y^2)dx/dy + (3x)(2y) dx/dy +3y^2 dx/dy = 0

I have all the dx/dy on one side... now what? This is where I went wrong and I do know know where...

Oh ok thanks alot, but when do you know to add the dy/dx beside one of the terms? I think that is where I am going wrong. - February 25th 2009, 02:43 PMSoroban
Hello, mathamatics112!

Quote:

We have: .

Then: .

. .

. .

. .

Quote:

We have: .

Then: .

. . . .

- February 25th 2009, 02:49 PMmathamatics112
Thank you very much, but I was wondering, When do you add the dy/dx? I put it in the wrong areas, which is why I am getting these answers wrong :http://mathhelpforum.com/calculus/75755-implicit-differentation.html#post272669\" rel=\"nofollow\">

So

Notice on the LHS you have a sum, and the derivative of a sum is the same as the sum of the derivatives. On the right you have a constant, and the derivative of a constant is 0.

So we have

.

The first part is a product, so we need to use the product rule. Since y is a function of x, we can find a derivative with respect to x, in terms of y. We do this using the chain rule.

Notice that . Also note that we are trying to FIND .

So, using these pieces of information we have

.

Hope that helped. Have a go of the second one yourself.