Find the derivatives of the function

Part B)

Part C)

Step-by-Step Explanation:

Question B)

We have:

And we want to find the derivative, h‘(t).

This will require the chain rule and the quotient rule. Remember that the chain rule states:

And the quotient rule:

Therefore, for our function h(t), we can let, by the chain rule:

Then by the quotient rule:

Then, by the chain rule, our derivative, h’(t), is:

Simplify:

Part C)

We have:

Again, we will utilize the chain rule. This time, we will let:

Then differentiating gives (on the right, we will apply the chain rule a second time):

To differentiate v(t), as mentioned, we need to apply the chain rule. We have:

We will let:

Therefore:

So:

And by simplification:

Therefore, it follows that:

So:

i believe the answer to be 48

step-by-step explanation: