00:01
Okay, to work out the tangent equation, the first thing you to know is the slope of a tangent, and you can find that by finding divide by dx, or in this case, f dash of x.
00:11
So differentiate this rational function.
00:16
We'll call this one u over v.
00:19
So use the quotient rule, as you will find on all the formula sheets for calculus.
00:25
So it's x minus 1 squared, x minus 1, x minus 1, times.
00:31
1 minus x plus 2 times 1.
00:36
In other words, what i'm doing here is v squared, v -u -dashed, uv -dashed, uv -dashed.
00:46
And that will simplify.
00:49
On top, i'm going to have x minus 1, minus x minus 2 over x minus 1 or squared.
00:59
So the x terms cancel out...