I am a 16 year old student who is due to start college. I need help with this question!

Find an expression in terms of x and y for dy/dx, given that:

y^3+(3x^2)y-4x=0

Any help would be greatly appreciated.

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- September 6th 2006, 11:23 AMShowcase_22Differentiation
I am a 16 year old student who is due to start college. I need help with this question!

Find an expression in terms of x and y for dy/dx, given that:

y^3+(3x^2)y-4x=0

Any help would be greatly appreciated. - September 6th 2006, 11:34 AMTD!
If it's hard to solve to the form y = f(x), you can use implicit differentiation and solve for y'(x).

In general, this will depend on both x and y, but that's allowed here :)

To check your answer, I find:

- September 6th 2006, 11:43 AMSoroban
Hello, Showcase_22!

This requires Implicit Differentiation.

I hope you're familiar with it.

Quote:

Find an expression in terms of and for

given that: .

We have: .

. . . . . . . . . . . . . . . . . . . .

Then: .

. . . . . Chain Rule . . Product Rule

Now solve for . . .

We have: .

Factor: .

Therefore: .

- September 6th 2006, 11:44 AMShowcase_22
How do you differentiate like that?

this is what i'm doing:

y^3+ (3x^2)y-4x=0

3y^2(dy/dx)+(3x^2)(2x(dy/dx))+3y-4=0

3y^2(dy/dx)+(3x^2)(2x(dy/dx))=4-3y

(dy/dx)((3y^2)+6x^3)=4-3y

dy/dx=(4-3y)/((3y^2)+6x^3)

It looks a little confusing like this, but the answer I get is a little wrong. How would you solve this? - September 6th 2006, 11:48 AMShowcase_22
Wow, thanks for your reply!

I worked on that question for an hour this morning whilst on the bus, I thought it was impossible!