# Whether the statement “ d 2 y d x 2 = ( d y d x ) 2 ” is true or false. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2, Problem 17RQ
To determine

## To find: Whether the statement “ d2ydx2=(dydx)2 ” is true or false.

Expert Solution

The statement “ d2ydx2=(dydx)2 ” false.

### Explanation of Solution

Given information:

The given statement is “ d2ydx2=(dydx)2 ”.

Calculation:

Consider the given statement.

d2ydx2=(dydx)2d2ydx2=ddx(dydx)

Now,

(dydx)2=(dydx)(dydx)

Therefore it is clear that d2ydx2(dydx)2 .

Let us assume a function y=x3+3x22 .

Differentiate the assumed function

dydx=3x2+6x …… (1)

Square equation (1).

(dydx)2=(3x2+6x)2(dydx)2=9x4+36x2+36x3 ….. (2)

Double differentiate the function.

d2ydx2=6x+6 . ….. (3)

It is clear from equation (2) and (3) that d2ydx2(dydx)2 .

Therefore, the statement “ d2ydx2=(dydx)2 ” is false.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!