BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 17RQ

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.

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