00:02
We're going to find the equation of the tangent line to the curve y equals square root 1 plus x cubed at the point to 3.
00:10
The slope of the tangent line will be the derivative at that point.
00:14
So let's start by finding the derivative.
00:16
And i'm going to rewrite y as 1 plus x cubed to the 1 half power.
00:21
And so then i can use the chain rule, starting with the derivative of the 1 half power function, bring down the 1⁄2, and raise 1 plus x cubed to the negative 1 half power.
00:31
And then we multiply that by the derivative of the inside.
00:34
The derivative of 1 plus x cubed is 3x squared.
00:39
Now we're evaluating this derivative at x equals 2.
00:43
We could simplify first or we could substitute the 2 in first and simplify after.
00:48
So that's what i'm going to do.
00:50
So i have 1�t times 1 plus 2 cubed to the negative 1⁄2 squared...