Step 1:

The function .

Apply derivative on each side with respect to x.

Apply power rule of derivatives .

Therefore derivative of is .

Step 1:

The function .

Apply derivative on each side with respect to x.

Apply the product rule of derivatives : .

Derivative of cosine function is  .

Therefore derivative of is .

Step 2:

The function is  .

Differentiate on each side with respect to x.

.

Quotient rule of derivatives .

Power rule of derivatives: and .

Therefore derivative of is .

Step 1:

The function .

Apply derivative on each side with respect to x.

Derivative of logarithm function is : .

Power rule of derivatives: .

Therefore derivative of is .

Step 1:

The function .

Apply derivative on each side with respect to x.

Apply power rule of derivatives .

Therefore derivative of is .

Step 1:

The function .

Apply derivative on each side with respect to x.

Derivative exponential function : .

Therefore derivative of is .

(7)

Step 1:

The function .

Apply derivative on each side with respect to x.

Apply the product rule of derivatives : .

Derivative of sine function is  .

Derivative of cot function is  .

Therefore derivative of is .