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00:00:00 – 00:06:28
The video tutorial explains how to find the first and second derivatives of y with respect to x in terms of t using parametric equations. The method involves calculating derivatives and simplifying expressions involving e^t. Emphasis is placed on the straightforward nature of the calculations despite the apparent complexity. The final results are presented as mathematical expressions involving exponential functions.
00:00:00
In this segment of the video, the instructor explains how to find the first derivative of y with respect to x in terms of t by using the parametric equations given. The first derivative is calculated as 1/2(e^(3t – 2t)), simplifying to t. The instructor then hints at using the same method to find the second derivative of y with respect to x.
00:03:00
In this segment of the video, the speaker explains how to find the second derivative of y with respect to x by taking the derivative of the first derivative with respect to t and dividing it by the derivative of x with respect to t. The process involves evaluating the derivative with respect to t of dy/dx over dx/dt. The speaker emphasizes that although this may seem complex, the calculations are straightforward, as shown by the example given with differentiation of e to the power of t.
00:06:00
In this segment of the video, the presenter explains a mathematical expression involving division by six and the exponential function e^t. The final result is simplified to one over 12 e to the t.