   Chapter 10.3, Problem 97E

Chapter
Section
Textbook Problem

True or False? In Exercises 97-100, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If x = f ( x )   and   y = g ( t ) ,   then   d 2 y d x 2 = g " ( t ) f " ( t )

To determine
Whether the statement “if x=f(t) and y=g(t), then d2ydx2=g(t)f(t)” is true or false.

Explanation

Consider the parametric equations, x=f(t) and y=g(t).

Differentiate x=f(t) with respect to t. To get,

dxdt=f(t)

Differentiate y=g(t) with respect to t. To get,

dydt=g(t)

To find out the ratio of the both of differentiation. So,

dydx=dydtdxdt=g(t)f(t)

Again, differentiate the above equation again with respect to x.

d2ydx2=ddt(dydx)dxdt=ddt(g(t)f(

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

In Exercises 1 and 2, simplify the expression. 4(10)75

Calculus: An Applied Approach (MindTap Course List)

Find dy/dx by implicit differentiation. 11. y cos x = x2 + y2

Single Variable Calculus: Early Transcendentals, Volume I

What is the value of (X + 1) for the following scores: 0, 1, 4, 2? a. 8 b. 9 c. 11 d. 16

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Factor each expression in Problems 7-18 as a product of binomials. 17.

Mathematical Applications for the Management, Life, and Social Sciences

Solve each equation and check: w712=3

Elementary Technical Mathematics

Find if , y = sin 2t.

Study Guide for Stewart's Multivariable Calculus, 8th 