# Homework Help: Derivative question! Exam tomorrow, need to understand this asap!

1. Oct 30, 2012

### nukeman

1. The problem statement, all variables and given/known data

Hey all!

Ok, doing a simple implicit differential.

x^3 + y^3 = 6xy

The 6xy is messing me up! How do I differentiate that??

The book says 6xy turns into 6y + 6xy'

I do not understand how to differentiate 6xy (how the x and y are stuck together)

Ok, doing a simple implicit differential.

2. Relevant equations

3. The attempt at a solution

2. Oct 30, 2012

### Mentallic

$$\frac{d}{dx}(xy)=\frac{dx}{dx}\cdot y + x\cdot \frac{dy}{dx}$$

Notice how it's the product rule?

3. Oct 30, 2012

### nukeman

Yes I know its the product rule....

Wait. Ahh, I see!!!

6x is f and y is g (in terms of f'g + fg')

which gives me

(6y) + 6x(y')

:)

Thanks!

4. Oct 30, 2012

### nukeman

But now that brings me to my 2nd question.

This leaves me with: x^2 + y^2y' = 2y + 2xy'

I don't understand how to solve for y' when I have 2 of them.

5. Oct 30, 2012

### Dick

Use algebra! Move both y' terms to one side of the equation everything else to the other side and solve for it.

6. Oct 30, 2012

### nukeman

ahhg, I think I need to stop. I am forgetting such silly things!!!!

I got the question. Thanks guys. Think its time for little break :)