(2)

Step 1:

The function is .

Apply derivative on each side with respect to .

Power rule of derivatives : .

.

.

Apply derivative on each side with respect to .

.

Apply derivative on each side with respect to .

. 

Solution :

The third derivative of the  function is .

(1)

Step 1 :

Thin sheet of ice is in the form of a circle.

Area of the circle is , where is the radius of the circle.

Area of the sheet is decreasing at rate of m²/sec.

Consider .

Differentiate on each side with respect to .

Determine the rate at which radius is decreasing when the area of the sheet is m².

Substitute and in . 

Therefore, the radius of the sheet ids decreasing at 0.0498 m/sec. 

Solution :

The derivative of the function is .

(3)

Step 1:

The function is .

Apply derivative on each side with respect to .

Product rule of derivatives : .

Power rule of derivatives : .

Derivative of the cosine function:.

.

Apply derivative on each side with respect to .

.

Solution :

The second derivative of the  function is .