00:01
We're going to find the equation of the tangent line at x equals 1 for f of x equal to 2 times the natural log of x cubed.
00:07
So we have the chain rule right here, and then we have this identity for a derivative of natural log.
00:17
So we're going to go ahead and change colors, and we'll start with the chain rule.
00:22
So f of u is equal to the natural log of u.
00:26
So f prime of u is equal to 1 over u u is equal to x cubed u prime equals 3x squared we can plug this in so f prime of x equals 2 times f prime of u of x so 1 over x cubed times u prime u times u prime which is 3x squared so we can clean this up a little bit, and it'll be 6x squared over x cubed.
01:11
So we need f prime of 1, which is equal to 6 times 1 squared over 1 cubed, which is equal to 6.
01:22
We also need a point.
01:25
So this is our slope.
01:27
We also need a point...