Question

Give the value of (d^2y/dx^2) at the point (0,1) given that x^2+2xy+2y^2=2.

Answer 1

There's my work so far. Do I just find the derivative of my answer now (second derivative)?

Answer 2

differentiate, solve for dy/dx, differentiate again, (where ever you have a dy/dx in this 2nd expression, sub.s in the result you got from the first differentiation)

Answer 3

yep, fine so far.

Answer 4

So basically I will take the derivative of the given equation ([-2x-2y]/[2x+4y]), find the derivative of that, and then plug in my points (0,1)?

Answer 5

you'll differentiate it again, yes. the trick is that when you differentiate, you'll have more dy/dx 's show up. that's when you use dy/dx =[-2x-2y]/[2x+4y]) to sub.s in, so that your final expression is only in terms of x and y.

Answer 6

Ah. So for any dy/dx answers, just plug in the formula for dy/dx from the first derivative?

Answer 7

yep.

Answer 8

Ok, sounds good. Thanks.

Answer 9

And I'm just gonna use the basic quotient rule to find this derivative, amiright?

Answer 10

yes

Answer 11

well, and the chain rule ofc.

Answer 12

Yes, true. Ok, thanks.

Answer 13

sure:)