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Question

Answer 1

(1)

Step 1:

The function .

Apply derivative on each side with respect to x.

Apply power rule of derivatives : .

Therefore derivative of is .

Solution :

.

Answer 2

(2)

Step 1:

The function .

Apply derivative on each side with respect to x.

Apply product rule of derivatives : .

Derivative of cosine function is  .

Therefore derivative of is .

Solution :

.

Answer 3

(3)

Step 1:

The function is .

Differentiate on each side with respect to x.

.

Quotient rule of derivatives .

Power rule of derivatives: and .

Therefore derivative of is .

Solution :

.

Answer 4

(4)

Step 1:

The function .

Apply derivative on each side with respect to x.

Derivative of logarithm function : .

Power rule of derivatives: .

Therefore derivative of is .

Solution :

.

Answer 5

(6)

Step 1:

The function .

Apply derivative on each side with respect to x.

Derivative of exponential function : .

Therefore derivative of is .

Solution :

.

Answer 6

(7)

Step 1:

The function .

Apply derivative on each side with respect to x.

Apply product rule of derivatives : .

Derivative of sine function is  .

Derivative of cot function is  .

Therefore derivative of is .

Solution :

.

Answer 7

(5)

Step 1:

The function .

Apply derivative on each side with respect to x.

Apply power rule of derivatives .

Therefore derivative of is .

Solution :

.