Solving a Calculus Problem with Implicit Differentiation

[Jason03]

Heres another problem I was working on...

http://img141.imageshack.us/img141/2318/calc2qg4.jpg

Im trying to find dy/dx using implicit differentiation...my algebra is a bit rusty...but I am trying to make sure I am on the right track...

 

[rocomath]

Implicit diff of x^2 is not 2xy', it's just 2x. Everything else is fine.

 

[Jason03]

where did I do that in the problem?

 

[Hitman2-2]

Not quite;

When you are differentiating x² with respect to x, for example, you simply get 2x. You do not multiply 2x by dy/dx.

However, when you (implicitly) differentiate y² with respect to x (where y is a function of x) you get

$$2y \frac{dy}{dx}$$

Here you do multiply by dy/dx; the reason comes from the chain rule.

 

[Hitman2-2]

where did I do that in the problem?

Third line, first expression on the left hand side (referring to your attached image)

 

[Jason03]

like this?

http://img375.imageshack.us/img375/5230/calc3eh3.jpg

 

[Jason03]

does the work above look ok?

 

[Hitman2-2]

does the work above look ok?

Looks fine to me