Download the App!

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

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Use the appropriate rules to determine the derivative.$$r=\frac{u}{3}+\frac{5}{u}-\frac{3 u-7}{4}, \text { find } \frac{d r}{d u}$$

$$\frac{-5}{12}-\frac{5}{u^{2}}$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 2

Derivatives Rules 1

Derivatives

Missouri State University

Oregon State University

University of Nottingham

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

02:01

Find the derivative of eac…

01:41

Use the appropriate rules …

01:47

Find the indicated derivat…

02:07

Find the derivative of the…

01:56

Differentiate the function…

02:42

uh, the way I would do this problem is just to rewrite. Ah, you over three plus five over you. Yeah. And then this other piece that's minus. And you may even want to do the quantity. I don't know if anybody really needs to. It won't affect your derivative. Okay, um, and if you're confused, how do you know you're finding the derivative? Well, DRD, you is a symbol for the derivative that does not look like you. But anyway, so I would do a little preliminary work of understand that you divide by three. Um, may I go ahead and rewrite those one third you plus five U to the negative first, and then rewrite. This is three forced you, uh, and divide each piece. So that's going to become plus, because of the negative in front seven force. Um, and the whole point of that, then is I can combine like terms here and here. So I'm looking at if I got the same denominator of 12 and 12. Well, one third is 4. 12 and 34 Should be 9, 12 and four minus nine would be negative. 5. 12. You five years and the first plus seven forces. So now I'm ready to take the drip that there was a lot of preliminary work because as you look at you to the first you multiply that one in front, it's just gonna be negative. 5. 12. As you move this negative one in front, it becomes minus five. You to the negative second and the derivative of a constant zero. So nothing too right there. And I would let my students leave their answer like this. That's just me. Because otherwise you can rewrite it just with a negative exponents, as over you squared as is accepted as well up to you, right?

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:55

Locate all critical points.$$f(x)=2 x^{4}+2 x^{3}-x^{2}-7$$

02:14

Determine the equation of the tangent line at the indicated $x$ -value.$…

02:21

(a) Find the $x$ -intercept(s); (b) Find the vertical asymptotes; (c) Find t…

03:41

Sometimes when one plots a set of data, it appears to be piece wise linear, …

02:02

Determine two simple functions who composition is $f g(x)$ ).$f(g(x))=\l…

01:08

You are given a pair of supply and demand equations; identify which is suppl…

02:28

Suppose two triangles are similar to each other and the first triangle has a…

02:08

The Floor and $C E I L I N G$ functions are defined as follows:$$\begin{…

01:10

Sketch the graph of a continuous function increasing on $-1<x<2$ and d…

00:51

Find $f^{\prime}(x)$.$$f(x)=2 x^{2}-7 x+9$$.