help? derivative[higher order]

Question

Answer 1

(6)

Step 1:

The function is .

Apply derivative on each side with respect to .

Power rule of derivatives:.

.

.

Step 2:

.

Apply derivative on each side with respect to .

Step 3:

Apply derivative on each side with respect to .

Step 4:

.

Apply derivative on each side with respect to .

Therefore, fourth derivative of the function .

Solution :

Fourth derivative of the function .

Answer 2

7)

Step 1:

The function is .

Apply derivative on each side with respect to .

Power rule of derivatives : .

Step 2:

.

Apply derivative on each side with respect to .

Step 3:

.

Apply derivative on each side with respect to . 

.

Step 4:

.

Apply derivative on each side with respect to .

Therefore, fourth derivative of the function is .

Solution :

Fourth derivative of the function is .

Answer 3

8)

Step 1:

The function is .

Apply derivative on each side with respect to .

.

Derivative of the sine function:.

Step 2:

.

Apply derivative on each side with respect to .

 

Derivative of the cosine function : .

.

Step 3:

.

Apply derivative on each side with respect to .

.

Step 4:

.

Apply derivative on each side with respect to .

.

Therefore, fourth derivative of the function is .

Solution :

Fourth derivative of the function .