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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.4, Problem 55E

(a)

To determine

**To find:** The derivative of

Expert Solution

The derivative of

**Given:**

The function is

**Result used: Chain Rule**

If *h* is differentiable at *x* and *g* is differentiable at *x* and

The slope of the line passing through the points

**Calculation:**

Obtain the value of

Apply the chain rule as shown in equation (1),

Substitute

From the given graph, it is observed that

From the given graph, the function

Obtain the values

Since the slope of the line at every point is equal, the slope of the function

Therefore, the value of

The slope of the function

Therefore, the value of

Substitute

Therefore, the value

(b)

To determine

**To find:** The value

Expert Solution

The function

**Given:**

The function is

**Calculation:**

Obtain the derivative of *.*

Apply the chain rule as shown in equation (1),

Substitute

From the graph observe that,

Obtain the slope of

From the given graph, it is observed that the function

Therefore, it can be concluded that the function

(c)

To determine

**To find:** The value

Expert Solution

The value

**Given:**

The function is

**Calculation:**

Obtain the derivative of *.*

Apply the chain rule as shown in equation (1),

Substitute

From the graph observe that,

The function

Obtain the value

Since the slope of the line at every point is equal, the slope of the function

Therefore, the value of

Obtain the value

The slope of the function

Therefore, the value of

Substitute

Therefore, the derivative of