How Do I Differentiate the Term 6xy in an Implicit Differentiation?

[nukeman]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[Mentallic]

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

Notice how it's the product rule?

 

[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!

 

[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.

 

[Dick]

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

 

[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 :)