00:01
What is the derivative of sine x squared over x squared? now i'm sure you all know the quotient rule and you could employ it swimmingly, but i really don't love doing that unless i have to.
00:12
So i prefer to rewrite it, and this is a trick that a lot of people use, a sine x squared, times x to the negative 2.
00:23
Because remember x to the negative 2 is the same as 1 over x squared.
00:29
That's just a little handy map that people use.
00:33
So now instead of doing the quotient rule, we can do the product rule.
00:38
Remember the product rule i write it up here is the first times the derivative of the second, plus the second times the derivative of the first.
00:50
So with that lovely rhyme in our minds, the first is sine x squared.
00:55
I'll write it all the way down here times the derivative of the second.
00:58
We bring the negative 2 in front, so negative 2x, and then add 1 becomes a negative 1, plus the second, which is just x to the negative 2, times the derivative of the first...