   Chapter 10, Problem 2RQ

Chapter
Section
Textbook Problem

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.2. If x = f(t) and y = g(t) are twice differentiable, then d 2 y d x 2 = d 2 y / d t 2 d 2 x / d t 2

To determine

To find: Whether the given statement is true or false and explain with an example if necessary to prove your answer.

Explanation

Given:

The parametric equation of the variable x is as follows.

x=f(t) (1)

The parametric equation of the variable y is as follows.

y=g(t) (2)

Calculation:

Differentiate y with respect to x we get, (first differentiation)

ddx(y)

ddx(y) (3)

Differentiate (3) with respect to x we get, (second differentiation)

ddx(ddx(y))

Multiply and divide by dt

=ddx(dydx)dtdt

=</

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