00:01
This question asks us to find the derivative of a given function.
00:04
To start off, we must look at the function, f of z is equal to cotangent inverse of the square root of z.
00:16
So because of this, we're going to have to use the chain rule, since we have square root of z and not just z inside of the parentheses.
00:23
So when evaluating the derivative f prime of z, we start off with the derivative of cotangent inverse.
00:32
This would be equal to negative 1 over 1 plus whatever is in the parentheses squared.
00:42
So what's in the parentheses is square root of z, so we'll write that here.
00:46
Then we multiply that by the derivative of square root of z.
00:50
To evaluate this, think of it as z to the one -half power.
00:57
Using the power rule, the derivative with respect to z of this would just be equal to one half z to the negative 1 over 2 power since we subtract 1 from it.
01:12
So that'll be what we multiply by, half z to the negative half.
01:21
This is separate.
01:23
All right, so now we want to do some simplifying.
01:26
So we can do one over...