Implicit Differentiation

[Wboyt]

Implicitly differentiate -4x[sup:2a4i977v]3[/sup:2a4i977v] + 3xy[sup:2a4i977v]3[/sup:2a4i977v] = -1

 

[tkhunny]

Well, do it. Let's see your efforts.

RBGTHGANH

 

[Wboyt]

Im not sure how to start please help

 

[tkhunny]

Use the Chain Rule and find this derivative:

(d/dx)(3x-5)^2

Use the Product Rule and find this derivative:

(d/dx)[(x-4)(4/x)]

Then we can talk.

 

[Wboyt]

Well I know to start with -12x[sup:27mutvjm]2[/sup:27mutvjm] but I do not know what to do with the + 3xy[sup:27mutvjm]3[/sup:27mutvjm]. I get confused as to how to separate it into dy/dx components.

 

[tkhunny]

That's why I gave you the Product Rule practice exercise.

1) We are assuming that y = f(x) in whatever neighborhood we are interested. We don't know what f is. That's why it's implicit. We just proceed as if we know enough.

2) Use the product rule on the expression. When you get to trying to find the derivative of y, think about #1.

 

[Rowallan]

This really confused me too until I found
http://justmathtutoring.com/
He makes it appear so simple

Any way I get
-12x^2 +3y^2 +3x .dy/dx. y
If I've understood

 

[tkhunny]

Given y = f(x),

\(\displaystyle \frac{d}{dx}3xy^2 = 3\frac{d}{dx}xy^2 = 3\left(x\cdot 2\cdot y\cdot \frac{dy}{dx} + y^{2}\cdot 1\right)\)

Product Rule and Chain Rule. That's all it is. You ARE close.

 

[Rowallan]

Sorry, I omitted the 2, this was a typo.

 

[tkhunny]

Iterestingly, typos are just as wrong as other wrong answers.

Be more careful.

 

[Rowallan]

I usually write using pen and paper and it is much easier to see what you are doing as I don't have Latex or anything similar to write maths on the computer.
Sorry for the mistake, typo or otherwise