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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.1, Problem 60E

(a)

To determine

**To find:** The *n*th derivative of the function.

Expert Solution

The *n*th derivative of the function

**Given:**

The function is

**Derivative rules:**

(1) Constant multiple rule:

(2) Power rule:

**Calculation:**

The first derivative of

By the power rule (2),

Thus, the first derivative of

The second derivative of

Apply the constant multiple rule (1) and the power rule (2),

Thus, the second derivative of

The third derivative of

Apply the constant multiple rule (1) and the power rule (2),

Thus, the third derivative of

From the first, second and the third derivatives of *k*th form of

Substitute *n* for *k* in the above equation, then the *n*th derivative of

Therefore, it can be concluded that the *n*th derivative of

(b)

To determine

**To find:** The *n*th derivative of the function.

Expert Solution

The *n*th derivative of

**Given:**

The function is

**Derivative rules:**

(1) Constant multiple rule:

(2) Power rule:

**Calculation:**

The first derivative of

Apply the power rule (2),

Thus, the first derivative of

The second derivative of

Apply the constant multiple rule (1) and the power rule (2),

Thus, the second derivative of

The third derivative of

Apply the constant multiple rule (1) and the power rule (2),

Thus, the third derivative of

The first, second and third derivatives of

Proceed in the similar way, the *n*th derivative of

Therefore, it can be concluded that the *n*th derivative of