Step 1: To find the second derivative of f(t), we need to differentiate the given function f'(t)

F t 9e 4t 2e t 69472

Name: f t 9e 4t 2e t 69472
Uploaded: 2021-05-07T16:40:03-08:00
Duration: 3 min 22 s
Channel: Gregory Higby
Description: f t 9e 4t 2e t 69472

Transcript

00:01 We're given this function, f of t, is equal to t squared times e to the negative 2t.

00:13 So the big thing in this one, we just find the first derivative is the product rule, because we have an independent variable to the left as well as an independent variable to the right of the product.

00:24 Now, as far as the second derivative goes, that means we're taking the derivative twice.

00:29 It's the derivative of the derivative.

00:33 There's another way of thinking of that.

00:34 So let's find the first derivative doing the product rule.

00:37 What you do is you take the derivative of the left side, which is 2t, and you leave the right side alone.

00:44 E to the negative 2t plus.

00:46 Now you leave the left side alone.

00:49 And you take the derivative of the right side, or the derivative of an exponential function is itself.

00:55 And then you have to multiply by the derivative of the exponent.

00:58 Now what might be smart is to factor out a 2, a t, and an e to the negative 2t in both of those terms.

01:09 So you'd be left with 1 minus.

01:13 So we took out one of those t's.