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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.3, Problem 26E

(a)

To determine

**To find:** The derivative of

Expert Solution

The first derivative of

The second derivative of

**Given:**

The function is

**Derivative rules:**

(1) Product Rule:

(2) Difference Rule:

**Calculation:**

Obtain the derivative

Apply the product rule (1) and simplify further,

Therefore, the first derivative of

Obtain the second derivative of

Apply the difference rule (2),

Apply the product rule (1),

Therefore, the derivative of

(b)

To determine

**To check:** The derivatives

Expert Solution

The derivatives are reasonable.

From part (a), the derivatives of

**Graph:**

Use the online graphing calculator to draw the graph of the functions as shown below in Figure 1.

Form Figure 1, it is observed that the function

The value of the derivative of the function at any point *x* can be estimated by drawing the tangent line at any point

Mark the slope of the tangent as a point in *y*-axis and the value of *x* as a point in *x*-axis in the graph of

Proceed in the similar way at several points and obtain the rough graph of the

Hence, it can be concluded that the derivative of the function

The value of the derivative of the function at any point *x* can be estimated by drawing the tangent line at any point

Mark the slope of the tangent as a point in *y*-axis and the value of *x* as a point in *x*-axis in the graph of

Proceed in the similar way at several points and obtain the rough graph of the

Hence, it can be concluded that the derivative of the function