 In this video, we provide the solution to question number 10 for practice exam 3 for math 1220, in which case we're given a parametric curve, x equals 2 plus 3t and y equals cos of 3t. And we have to first calculate the derivative of this parametric curve, so the derivative dy over dx. And then we're also allowed to do the second derivative, d squared y over dx squared. Okay, so let's do the first part first. The formula for dy over dx is dy over dt divided by dx over dt. So we take the derivatives of these things. We start with the top. The derivative of y, which is cos of 3t, will be 3 cinch of 3t. The derivative of cos is cinch, not negative cinch. The derivative of x, when you take the derivative of constant, that would just be 0. So the derivative on the bottom is just 3. So this will simplify to be cinch of 3t. So that's the answer to the first part, cinch of 3t. Now be aware, this is your derivative there, y prime. So then when we come down here to this next part, to find the derivative, the second derivative here, we have to take the derivative of y prime with respect to t and divide that by the derivative of x with respect to t. Now we don't just take the second derivative of y with respect to t divided by the second derivative of x with respect to t. We take the derivative of y prime with respect to t and divide that by the derivative of x with respect to t. Now we already did the derivative of x with respect to t. That's just a 3. That's just going to go down there. So we need to take the derivative of cinch of 3t, for which that's going to be 3 cos of 3t. Don't forget the h there, 3t over 3. The 3's cancel again, and so then we end up with the second derivative being cos of 3t. So we then have the first and second derivative that was now calculated.