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__[The Problem]__We know:

r(t) = <3t

^{2}- 8t + 3, -9t

^{2}+ 2t + 7>

And we are asked to find d

^{2}y/dx

^{2}.

__[Background Information]__My understanding of d

^{2}y/dx

^{2}is that it is the

__second derivative with respect to x__(the first derivative of the function having been with respect to both x and y).

In other words, it's broken down like this:

(d/dx)(dy/dx) = d

^{2}y/dx

^{2}

The derivative (with respect to x) of the first derivative of the parametric function, r(t), is equal to that mess on the right hand side of the equation.

__[Attempt at a Solution]__So we know that:

(dy/dx) = (dy/dt) / (dx/dt) (From the textbook.)

And the above function, r(t), can be broken down into two parts:

x(t) = -9t

^{2}+ 2t + 7

y(t) = 3t

^{2}- 8t + 3

Therefore:

(dx/dt) = 6t - 8

(dy/dt) = -18t + 2

And

(dy/dx) = (-18t + 2) / (6t - 8)

So, now, here's where I feel like I'm guessing a little bit. Following that logic, would d

^{2}y/dx

^{2}= (6) * [(-18t + 2)/(6t - 8)]?

Heh, this is probably a silly question, but thanks very much in advance for any help!