/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 10 Give three different notations f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 10

Give three different notations for the derivative of \(f\) with respect to \(x\)

Short Answer

Expert verified
Question: Provide three different notations for the derivative of a function f with respect to x. Answer: The three notations for the derivative of a function f with respect to x are: 1. Leibniz notation: \(\frac{df}{dx}\) 2. Lagrange notation (Prime notation): \(f'(x)\) 3. Newton notation: \(\dot{f}(x)\)

Step by step solution

01

Notation 1: Leibniz Notation

Leibniz notation expresses the derivative of function f with respect to x using the symbol \(\frac{d}{dx}\). This notation highlights the change of the function as the change in x approaches zero. The derivative of f with respect to x using Leibniz notation is: $$\frac{df}{dx}$$
02

Notation 2: Lagrange (Prime) Notation

Lagrange notation represents the derivative of the function f with respect to x using a prime symbol (') after the function name. This notation emphasizes the idea of the first derivative as a new function of x. The derivative of f with respect to x using Lagrange notation is: $$f'(x)$$
03

Notation 3: Newton Notation

Newton notation demonstrates the derivative of function f with respect to x by placing a dot above the function name. This notation is less common but can be found in some scientific fields such as physics. The derivative of f with respect to x using Newton notation is: $$\dot{f}(x)$$

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Quotient Rule for the second derivative Assuming the first and second derivatives of \(f\) and \(g\) exist at \(x\), find a formula for \(\frac{d^{2}}{d x^{2}}\left[\frac{f(x)}{g(x)}\right]\)

Suppose \(y=L(x)=a x+b\) (with \(a \neq 0\) ) is the equation of the line tangent to the graph of a one-to-one function \(f\) at \(\left(x_{0}, y_{0}\right) .\) Also, suppose that \(y=M(x)=c x+d\) is the equation of the line tangent to the graph of \(f^{-1}\) at \(\left(y_{0}, x_{0}\right)\) a. Express \(a\) and \(b\) in terms of \(x_{0}\) and \(y_{0}\) b. Express \(c\) in terms of \(a,\) and \(d\) in terms of \(a, x_{0},\) and \(y_{0}\) c. Prove that \(L^{-1}(x)=M(x)\)

Multiple tangent lines Complete the following steps. a. Find equations of all lines tangent to the curve at the given value of \(x\) b. Graph the tangent lines on the given graph. \(4 x^{3}=y^{2}(4-x) ; x=2\) (cissoid of Diocles)

Suppose your graphing calculator has two functions, one called sin \(x,\) which calculates the sine of \(x\) when \(x\) is in radians, and the other called \(s(x),\) which calculates the sine of \(x\) when \(x\) is in degrees. a. Explain why \(s(x)=\sin \left(\frac{\pi}{180} x\right)\) b. Evaluate \(\lim _{x \rightarrow 0} \frac{s(x)}{x} .\) Verify your answer by estimating the limit on your calculator.

Graphing \(f\) and \(f^{\prime}\) a. Graph \(f\) with a graphing utility. b. Compute and graph \(f^{\prime}\) c. Verify that the zeros of \(f^{\prime}\) correspond to points at which \(f\) has \(a\) horizontal tangent line. $$f(x)=\left(x^{2}-1\right) \sin ^{-1} x \text { on }[-1,1]$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.