final pratice exam help please no calculator

Question

Answer 1

(10)

The function is .

Apply derivative with respect to x .

Use the product rule of derivatives .

Option (a) is correct .

Comments

Okay so I have 2 questions that I am confused on.

 

1. Step 2: How is it when you deriave step 1 radical it becomes 1/2 radical 2x-3? I see on the right you showed me a rule. Is it when you apply that to any radicals?

 

2. Step 4 to 5, how do you do that algebraically? How you add so it becomes the 5th step? How you get rid of the radical so you can combine it to become step 5. You skip a step inbetween so I can't understand it.

 

Thanks

---

(1)

Yes that is the rule applied.

or simply you can make use of power rule of derivatives

can be written as

Now apply power rule.

---

(2)

Multiply and divide by .

This is how we get.

Answer 2

(11)

The function is .

Apply derivative with respect to x .

Use the power rule of derivatives .

Option (d) is correct .

Comments

I am a bit confused from the 3rd last step with the 1's. 1-1/(-1)^2. -1 powered is 1. 1/1 is 1. 1-1=0. However on the 2nd to last step, you have -1. Why is that? CONFUSED

---

Yes, that is what is done in the last second step.

For better understanding, see the following steps.