00:01
In this problem, we are beginning to get comfortable with taking first derivatives.
00:06
Specifically, we are now making the connection between derivatives and its applications, specifically with finding velocity.
00:14
So we are given a function f of t, and f of t equals 10 plus 45 all over t plus one.
00:22
And we're told find the velocity given that this equation is the position.
00:26
Now, what do we know about the relationship between position and velocity? velocity is the first derivative of position.
00:34
So what this problem is essentially asking you is to simply take the first derivative of f of t.
00:39
So we have to find f prime of t.
00:43
Now the first thing to note is that the derivative of a constant is 0.
00:47
And here we have a quotient.
00:49
So we're going to be using quotient rule.
00:51
So f prime of t is going to be equal to negative 45 times the derivative of t plus the derivative of 1 all over t plus 1 squared...