help derivatives? higher order

Question

Answer 1

4)

Step 1:

The function is .

Apply the formulae of derivatives:

.

Consider .

Apply the derivative on each side with respect to .

.

Step 2:

Again apply the derivative on each side with respect to .

Again apply the derivative on each side with respect to .

Third derivative of is .

Solution:

Third derivative of is .

Answer 2

5)

Step 1:

The function is .

Apply derivative on each side with respect to .

Apply the formula .

.

Step 2:

Again apply the derivative on each side with respect to .

 Apply the product rule in derivatives : .

.

Step 3:

Apply derivative on each side with respect to .

.

.

Solution:

Third derivative of is .