   Chapter 10, Problem 25RE

Chapter
Section
Textbook Problem

# Find dy/dx and d2y/dx2.25. x = t + sin t, y = t − cos t

To determine

To find: The expression of dydx and d2ydx2 for x=t+sint and y=tcost .

Explanation

Given:

The parametric equation for the variable x is as follows.

x=t+sint (1)

The parametric equation for the variable y is as follows.

y=tcost (2)

Calculation:

Differentiating (1) with respect to t we get,

dxdt=1+cost (3)

Differentiating (2) with respect to t we get,

dydt=1+sint (4)

Dividing equation (5) by (3) we get,

dydx=1+sint1+cost (5)

Differentiating (5) with respect to t we get,

d2ydx2=ddt(dydx)dxdt (6)

Substitute equation (3) and (5) in (6) we get,

d2ydx2=ddt(1+sint1+cost)1+cos

### 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

#### y=4x2+1 defines y implicitly as a function of x.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### True or False: converges.

Study Guide for Stewart's Multivariable Calculus, 8th

#### Explain why plagiarism is unethical.

Research Methods for the Behavioral Sciences (MindTap Course List) 