00:01
Okay, so to find this derivative, the first thing we want to do is change this from z times tan z to z times sine of z divided by cosine of z.
00:11
And so now we can use, we can do a, let's just do a quotient rule here to find this derivative.
00:19
So the quotient rule tells us that the derivative of a fraction where we have our variable in both the numerator and the denominator is going to be equal to the derivative of the numerator, which is, we're going to have to use a product rule to actually find.
00:33
So that's going to be sine of z plus z times cosine of z.
00:40
And then this is multiplied by the denominator, since this was the derivative of the numerator, multiplied by the denominator, and then minus the numerator, multiplied by the derivative of the denominator, and the derivative of the denominator is equal to negative sine of z.
00:55
So this is actually going to be plus z times sine squared of z.
01:01
And this is divided by the denominator squared, which is cosine squared of z...