IMPLICIT DIFFERENTIATION

[belowdefeat]

The curve with equation 2(x^2 + y^2)^2 = 25(x^2 - y^2) is called a lemniscate. Find dy/dx.

I tried going:

4(x^2 + y^2) = d/dx 25(x^2 - y^2)
but don't know what to do from here, or if this is even correct.

 

[Deleted member 4993]

The curve with equation 2(x^2 + y^2)^2 = 25(x^2 - y^2) is called a lemniscate. Find dy/dx.

I tried going:

4(x^2 + y^2) = d/dx 25(x^2 - y^2).... This is wrong
but don't know what to do from here, or if this is even correct.

d/dx [2(x[sup:w5zr2d8l]2[/sup:w5zr2d8l] + y[sup:w5zr2d8l]2[/sup:w5zr2d8l])[sup:w5zr2d8l]2[/sup:w5zr2d8l]] = d/dx [25(x[sup:w5zr2d8l]2[/sup:w5zr2d8l] - y[sup:w5zr2d8l]2[/sup:w5zr2d8l])]

4[(x[sup:w5zr2d8l]2[/sup:w5zr2d8l]+y[sup:w5zr2d8l]2[/sup:w5zr2d8l])(2x + 2y*y')] = 25(2x - 2y*y')

Now simplify and solve for y'.

 

[belowdefeat]

OH! i get it now thanks dude! chain rule.

 

[belowdefeat]

so the answer is:

dy/dx = [x[25 - 4(x^2 + y^2)]] / [y[25 + 4(x^2 + y^2)]] ?

 

[Deleted member 4993]

The curve with equation 2(x^2 + y^2)^2 = 25(x^2 - y^2) is called a lemniscate. Find dy/dx.

I tried going:

4(x^2 + y^2) = d/dx 25(x^2 - y^2).... This is wrong
but don't know what to do from here, or if this is even correct.

d/dx [2(x[sup:3ibp0z81]2[/sup:3ibp0z81] + y[sup:3ibp0z81]2[/sup:3ibp0z81])[sup:3ibp0z81]2[/sup:3ibp0z81]] = d/dx [25(x[sup:3ibp0z81]2[/sup:3ibp0z81] - y[sup:3ibp0z81]2[/sup:3ibp0z81])]

4[(x[sup:3ibp0z81]2[/sup:3ibp0z81]+y[sup:3ibp0z81]2[/sup:3ibp0z81])(2x + 2y*y')] = 25(2x - 2y*y')

Now simplify and solve for y'.

4[(x[sup:3ibp0z81]2[/sup:3ibp0z81]+y[sup:3ibp0z81]2[/sup:3ibp0z81])(2x + 2y*y')] = 25(2x - 2y*y')

8x(x[sup:3ibp0z81]2[/sup:3ibp0z81]+y[sup:3ibp0z81]2[/sup:3ibp0z81]) + y' * 8y(x[sup:3ibp0z81]2[/sup:3ibp0z81]+y[sup:3ibp0z81]2[/sup:3ibp0z81])= 50x - y' * 50y

y' * 8y(x[sup:3ibp0z81]2[/sup:3ibp0z81]+y[sup:3ibp0z81]2[/sup:3ibp0z81]) + y' * 50y = 50x - 8x(x[sup:3ibp0z81]2[/sup:3ibp0z81]+y[sup:3ibp0z81]2[/sup:3ibp0z81])

y' = [25x - 4x(x[sup:3ibp0z81]2[/sup:3ibp0z81]+y[sup:3ibp0z81]2[/sup:3ibp0z81])] / [25y + 4y(x[sup:3ibp0z81]2[/sup:3ibp0z81]+y[sup:3ibp0z81]2[/sup:3ibp0z81])]

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