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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.5, Problem 31E

To determine

**To calculate: **The second derivative of the function

Expert Solution

The second derivative of the function is

**Given information:**

The function

**Formula used:**

The chain rule for differentiation is if f is a function of g then

Power rule for differentiation is

Quotient rule for differentiation is

**Calculation:**

Consider the function

Differentiate both sides with respect to x ,

Recall that power rule for differentiation is

Apply it. Also observe that y is a function of x,

Isolate the value of

Therefore, the value of first derivative of the function is

Now, again differentiate the above expression with respect to x . Recall that quotient rule for differentiation is

Apply it. Also observe that y is a function of x,

Now, substitute the value

According to the question

Thus, the second derivative of the function is