Open In App

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 2: Q. 54 (page 210)

Suppose that r is an independent variable, s is a function of r, and q is a constant. Calculate the derivatives in Exercises 53– 58. Your answers may involve r, s, q, or their derivatives.
$\frac{d}{d r} r^{3}$

Short Answer

Expert verified

$\frac{d}{d r} r^{3} = 3 r^{2}$

Step by step solution

Step 1. Given Information

We need to find $\frac{d}{d r} r^{3}$

Step 2. Finding Derivative

$\frac{d}{d r} r^{3} = 3 r^{2}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line that is perpendicular to the tangent line to $f (x) = x^{4} + 1$ at $x = 2$ and also passes through the point $(- 1, 8)$

A bowling ball dropped from a height of $400$ feet will be $s (t) = 400 - 16 t^{2}$ feet from the ground after $t$ seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:

After $t = 1$ seconds, with $h = 0.5, h = 0.25, h = - 0.5 a n d h = - 0.2$

Use the limit you just found to calculate the exact slope of the tangent line to $f (x) = x^{2}$ at $x = 4$ . Obviously you should get the same final answer as you did earlier.

When the bowling ball hits the ground, with $h = - 0.5, h = - 0.2 a n d h = - 0.1$

Use the definition of the derivative to find $f$ for each function $f$ in Exercises $39 - 54$

$f (x) = \frac{1}{x^{2} - 1}$

See all solutions

Recommended explanations on Math Textbooks

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free

Suppose that r is an independent variable, s is a function of r, and q is a constant. Calculate the derivatives in Exercises 53– 58. Your answers may involve r, s, q, or their derivatives.
$\frac{d}{d r} r^{3}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding Derivative

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Company

Product

Help

Suppose that r is an independent variable, s is a function of r, and q is a constant. Calculate the derivatives in Exercises 53– 58. Your answers may involve r, s, q, or their derivatives.ddrr3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding Derivative

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Suppose that r is an independent variable, s is a function of r, and q is a constant. Calculate the derivatives in Exercises 53– 58. Your answers may involve r, s, q, or their derivatives.
$\frac{d}{d r} r^{3}$