The problem is from an online homework assignment. I know it's probably fairly simple, but my brain isn't grasping it right now for some reason. [The Problem] We know: r(t) = <3t2 - 8t + 3, -9t2 + 2t + 7> And we are asked to find d2y/dx2. [Background Information] My understanding of d2y/dx2 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) = d2y/dx2 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) = -9t2 + 2t + 7 y(t) = 3t2 - 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 d2y/dx2 = (6) * [(-18t + 2)/(6t - 8)]? Heh, this is probably a silly question, but thanks very much in advance for any help!