help-derivative-higher order

Question

Answer 1

(1)

Step 1:

The function is .

Apply the formulae of derivatives:

.

Apply derivative on each side with respect to .

         

       

.

Step 2:

Again apply derivative on each side with respect to .

The second derivative is .

Solution:

The second derivative is .

Answer 2

(2)

Step 1:

The function is .

Apply derivative on each side with respect to .

Apply formula: .

.

Step 2:

Again apply derivative on each side with respect to .

Apply quotient rule in differentiation: .

The second derivative is .

Solution:

The second derivative is .

Answer 3

(3)

Step 1:

The function is .

Apply derivative on each side with respect to .

.

Step 2:

Again apply derivative on each side with respect to .

.

The second derivative is .

Solution:

The second derivative is .