Good morning. I hope you are staying safe. I have to calculate the derivatives of the three functions. Also, I need to explain why these functions are Riemann integrable, which is something I'm definitely lost on. Problem 7.1. Calculate the following derivative:dte" dt =1dr-x²arctan(r)Problem 7.2. Calculate the following derivative:rx³ cos(x*)de--r'sin(x2)*dtdrProblem 7.3. Calculate the following derivative:sin(u?)np--du ) |r=r0ddret 2 dtWhy are the involved functions Riemann integrable?

Answered: Problem 7.1. Calculate the following…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Good morning. I hope you are staying safe. I have to calculate the derivatives of the three functions. Also, I need to explain why these functions are Riemann integrable, which is something I'm definitely lost on.

Problem 7.1. Calculate the following derivative:
d
te" dt =1
dr
-x²
arctan(r)
Problem 7.2. Calculate the following derivative:
rx³ cos(x*)
d
e-
-r'sin(x2)
*dt
dr
Problem 7.3. Calculate the following derivative:
sin(u?)
np-
-du ) |r=r0
d
dr
et 2 dt
Why are the involved functions Riemann integrable?

Expert Solution

Step 1

As per pur guidelines we are supposed to solve only one problem . The first problem has been solved in detail. We have used leibnitz rule to solve the problem. Follow the next steps for the solution.