Implicit Differentiation

[lamaclass]

Hi, I need help with getting started on this problem. I've worked out to set up the left side of it but am cofused on the right side of it. Thanks!

3(x[sup:2xrjyuxe]2[/sup:2xrjyuxe]+y[sup:2xrjyuxe]2[/sup:2xrjyuxe])[sup:2xrjyuxe]2[/sup:2xrjyuxe]=100(x[sup:2xrjyuxe]2[/sup:2xrjyuxe]-y[sup:2xrjyuxe]2[/sup:2xrjyuxe])

Here's what I've done so far:

6(x[sup:2xrjyuxe]2[/sup:2xrjyuxe]+y[sup:2xrjyuxe]2[/sup:2xrjyuxe])(x[sup:2xrjyuxe]2[/sup:2xrjyuxe]*2y*dy/dx+y[sup:2xrjyuxe]2[/sup:2xrjyuxe]*2x)=?

 

[wjm11]

3(x^2+y^2)2=100(x^2-y^2)

Here's what I've done so far:

6(x^2+y^2)(x^2*2y*dy/dx+y^2*2x)=?

Why are you using the Product Rule?

3(x^2+y^2)^2=100(x^2-y^2)
6(x^2+y^2)(2x + 2y(dy/dx)) = 100(2x - 2y(dy/dx))

Continue.

 

[lamaclass]

Thanks for your help! I actually am not sure why I used Product Rule for the first part now that I look at it again. For the second part, which rule did you apply?

ETA: Never mind, I see now that it was the Constant Multiple Rule that you used. Thanks again!