1. Differentiate

(1)

Solution: We know

(2)

We can use product rule to write

(3)

We also have the option to write the original function

(4)

and so

(5)

2. Differentiate

(6)

Solution: We can use the quotient rule

(7)

One can simplify (if needed).

3. Differentiate

(8)

Solution: We can write

(9)

Therefore

(10)

One can simplify when needed.

4. Find

(11)

Solution: We write

(12)

5. Differentiate

(13)

Solution: We use chain rule

(14)

6. Differentiate

(15)

Solution: We use chain rule

(16)