Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Find the $ n $ th derivative of each function by calculating the first few derivatives and observing the pattern that occurs.(a) $ f(x) = x" $ (b) $ f(x) = 1/x $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Clarissa Noh

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

02:00

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

02:49

Find the nth derivative of…

04:20

'Find the nth derivat…

05:12

Find the $m$ th derivative…

01:20

Compute $f^{\prime \prime}…

03:58

05:34

Find the $n$ th derivative…

he It's clear. So in new Marine here. So we're gonna find the first few derivatives you have ever X is equal to X to the end power when we have our first derivative, which is X and times X to the n minus one power. We have our second derivative, which is n times and minus one X to the N minus two. And we see that, uh, to the then power derivative is equal to and times and minus one times and minus two all the way. Tow n minus and close one times X to the n minus. And and this becomes equal to in factorial For part B, we're gonna do the same thing. Just write a couple of derivatives to see the pattern. X Square becomes next for the second er, bit of negative one negative too. Next to the negative three years power. And then we have, uh, then derivative, which is equal to negative one times Negative too, comes negative three all the way to negative and times X to the negative and plus one power which is equal to negative one to the end. Power factorial over X to the end, plus one

View More Answers From This Book

Find Another Textbook

03:29

4. [10 points] Find an orthogonal matrix Q that diagonalizes $ = S = QAQT .<…

03:17

Find singular value decompositions for the matrices listed in Exercises 7 th…

05:55

Integrate each of the following functions using substitution, finding the mo…

02:17

Question 101 ptsA very large rectangular area is to fenced in and di…

01:14

Find an equation for the hyperbola satisfying the following conditions. Grap…

02:12

0M1 points Previous Answers SPreCalc7 11.2.045Find an equation for the…

01:28

Clickto see additionalinstructions The histogram below represents scores ach…

03:19

17. Consider the dynamical system x' = Ax; where A = 55: Then the o…

03:05

Let t1,t2,tm be distinct positive integers, and let qn In(t1,t2, tm)…

02:22

-101010Use the image to answer the question:Find the compone…