nd and when

To find for the function , we’ll use the quotient rule. The quotient rule states that if you have a function , then the derivative is given by .

Here, and . Therefore, and .

Using the quotient rule:

Now to find :

Next, we calculate by differentiating :
Let’s utilize the quotient rule again:

for and .

Differentiating these will give and yields .

Now applying the quotient rule for :

This derivatives can get quite tricky! Let’s compute (after substituting ):

Eventually, you would find that:

Both derivatives indicate how the function behaves, whether it’s leveling out (critical point) or curving up and down (concavity). Happy calculating!