Prove the power rule d dx x n nx n1 for the case where n r s is a rational number ...

Prove the power rule d/dx[x n ] = nx n1 for the case where n = r/s

Question:

Prove the power rule d/dx[xⁿ] = nxⁿ⁻¹ for the case where n = r/s is a rational number.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus For Business, Economics And The Social And Life Sciences

ISBN: 9780073532387

11th Brief Edition

Authors: Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price

See More Books

Question Posted: May 28, 2023 04:29 AM

Prove or disprove that there is a rational number x and an irrational number y such that xy is irrational.
Use the Derivative Quotient Rule to prove the Power Rule for negative integers, that is, where m is a positive integer. d dx (_X) || -mx-m-1
Prove that if r and s are rational numbers, then r + s is a rational number. Start of Proof: Let r = p/q and s = u/v for some integers p, q, u, v where q and v arent equal to zero.
inary Differential Equations > Assessment 10.1-10.2 Score: 0.25/3 1/3 answered "X" Question 2 < Submit Question > Gradebook Convert the differential equation `u" -3 u' -4 u = e^(-t)` into a system of...
Vince Perez opened a law office on April 1, 2015. During the first month of opera-tions, the business completed the following transactions: Apr. 1 Perez contributed $ 62,000 cash to the business,...
Consider the following sample: a. Calculate the mean and standard deviation for this data. b. Determine the percentage of data values that fall in each of the following intervals: x s, x 2s, x 3s....
In July 2008, Brian, Dale, and Sandra Allen signed a contract with East Resources, Inc., concerning 148 acres of the Allens property. East wanted to develop and exploit the oil and gas resources...
Consider the following four LP formulations. Using a graphical approach, determine (a) Which formulation has more than one optimal solution. (b) Which formulation is unbounded. (c) Which formulation...
quick question are they same " the function of database management system and the characteristics of database management system? explain maintaining data integrity and give simple explanation to...
Use a graphing utility to graph the curve 5x 2 2xy + 5y 2 = 8. Draw the tangent line to the curve at (1, 1). How many horizontal tangent lines does the curve have? Find the equation of each...
A medical research team determines that t days after an epidemic begins, people N(t) = 10t 3 + 5t + t people will be infected, for 0 t 20. At what rate is the infected population increasing on the...
Use the information in Exercise to prepare an October 31 statement of cash flows for Ernst Consulting. Also assume the following: a. The owners initial investment consists of $38,000 cash and $46,000...
Discuss on what grounds an intervention order would be granted in South Australia and discuss the difference between criminal and civil legislation in relation to intervention orders. You are working...
Find the largest interval containing x = 0 that the Remainder Estimation Theorem allows over which f(x) = sin(3x) can be approximated by p(x) = 3x - decimal-place accuracy throughout the interval....
GBC Inc. experiences a loss of $100000 in 2022 and therefore cannot pay any dividends to shareholders. How will this development affect the value of shareholder's equity on the GBC Inc. Statement of...
Briefly explain the theory of Convergence relating to Economic Growth? How does Absolute Convergence differ from Conditional Convergence?
A client is unhappy with her former lawyer's account. She plans to complain to the Law Society that the lawyer has charged an excessive fee, and ask the Law Society to reduce the amount. a. Explain...
Based on the data in Table 6E.6 if an np chart is to be established, what would you recommend as the center line and control limits? Assume that n = 500. %::
State whether each statement is true or false. If false, give a reason. {purple, green, yellow} = {green, pink, yellow}
A campground owner has 1400 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing needed along the river. (See the sketch.) Let x represent the width of the field....
Use the differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the difference in the two results to 4 decimal places. 0.99
Find dy/dx by implicit differentiation for the following. x 4 y 3 + 4x 3/2 = 6y 3/2 + 5
Hugh works in a fishing packing plant at Rocky Bay in British Columbia. He works 20 hours per week, 40 weeks a year, and earns $18 per hour. Use claim code 2. Find his weekly gross salary, find the...
ane, a partner in a CPA firm, wishes to borrow money from Company A, which her CPA firm audits. She is a covered member with respect to Company A. Which type of loan would be most likely to impair...
Case Study: Global Net Ltd is an internet service provider in Australia which employs staff locatedoverseas to man its call centres. It has been operating in the business for three years.Competition...

Prove the power rule d/dx[x n ] = nx n1 for the case where n = r/s

Question:

Step by Step Answer:

y x5 or y x 1did...View the full answer

Calculus For Business, Economics And The Social And Life Sciences

Students also viewed these Mathematics questions