1. ## Differentiation and tangents

Hello all,

I am having trouble with the following:

Given the plane curve:
y^4 + 2x^2 - 2y^2 = 0

Find the equation for the slope of the tangent line to the curve.

I think you use implicit differentiation, but it is not covered very well in my textbook, and am going mental trying to figure this out!

Any help is much appreciated,

Dranalion.

2. Originally Posted by Dranalion
Hello all,

I am having trouble with the following:

Given the plane curve:
y^4 + 2x^2 - 2y^2 = 0

Find the equation for the slope of the tangent line to the curve.

I think you use implicit differentiation, but it is not covered very well in my textbook, and am going mental trying to figure this out!

Any help is much appreciated,

Dranalion.
Using the chain rule: $\frac{d}{dx} (y^n) = n y^{n - 1} \cdot \frac{dy}{dx}$.

3. Does this give:

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

I don't know where to go from here!

Any help is much appreciated!

4. Originally Posted by Dranalion
Does this give:

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

I don't know where to go from here!

Any help is much appreciated!
Where have the red x's come from? I don't see any x's in the formula I gave you ....?

Spoiler:
(4y^3) dy/dx + 4x - (4y) dy/dx = 0. Treat dy/dx as the unknown and make it the subject.

5. Mr fantastic's point is: Don't use "x" as a variable and to represent multiplication in the same equation. In fact, even if there doesn't happen to be an "x" in the equation it is very confusing to use "x" to represent multiplication. Use standard algebra notation instead.

6. Does dy/dx = -4x/(4y^3 - 4y) ?

7. Originally Posted by Dranalion
Does dy/dx = -4x/(4y^3 - 4y) ?
Yes. And this can be simplified a fair bit.