00:01
First we want to find the derivative of t with respect to x, and you could do this two ways, either with product rule or chain rule.
00:07
I'm going to use product rule because we have expression one and expression two, multiply by each other.
00:14
So first, we're going to take the derivative of the first expression, which is 2x using power rule, multiply that by the entire second expression, and then add the original first expression, multiply that by the derivative of the second, an expression.
00:31
Remember, one is a constant, so the derivative of that is zero, and you have technically one -ninth times x is the same as x over nine.
00:40
So that will give you one -ninth.
00:44
And then if you simplify, you'll get 2x minus one -ninth, x squared times dx.
00:57
So now looking at your original values, you start off with two, three, and four millimeters.
01:05
And want to see the change as it goes to 3 .2 .1, 3 .1 and 4 .1.
01:16
So with these values, first we need to find dx, which is basically your change from your original amount to your new amount.
01:23
And in all of these cases, it is 0 .1 millimeters...