help - product rule/quotient rule

Question

Answer 1

1)

The function .

Differentiate on each side with respect to .

.

Product rule of derivatives: .

Power rule of derivatives: and .

Solution:

.

Answer 2

2)

The function is .

Differentiate on each side with respect to .

.

Quotient rule in derivatives .

Power rule of derivatives: and .

Solution:

.

Answer 3

3)

The function is .

Differentiate on each side with respect to .

.

Product rule of derivatives: .

.

Power rule of derivatives: and .

.

Solution:

.

Answer 4

4)

The function .

Differentiate on each side with respect to .

.

Quotient rule in derivatives .

Power rule of derivatives: and .

.

Solution:

.