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

Find $d r / d u$ if $r=\frac{20}{\sqrt{5 u^{2}+9}}$

$$\frac{-100 u}{\left(5 u^{2}+9\right)^{3 / 2}}$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 6

The Chain Rule

Derivatives

Campbell University

Oregon State University

Harvey Mudd College

Baylor University

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.

01:09

Solve.$$\sqrt{9 r^…

00:48

Solve.$$\sqrt{r^{2}-8 …

00:49

$\sqrt{r^{2}+9 r+15}-r-4=0…

02:34

Find the value of $r$, if …

01:29

Find $d y / d u, d u / d x…

01:06

If ${ }^{20} C_{r}={ }^{20…

00:38

Solve using the square roo…

0:00

Solve.$\sqrt{8+2 r}=\s…

02:56

Evaluate the expression.

00:55

If $2^{r+5}=2^{2 r-1},$ wh…

uh, we're still doing the chain role for this problems derivative. I have a lot of students that would look at this and think the quotient rule right away because of the questions. Let me try and convince you. Three chain rule is better because I can rewrite this problem at the 20 is fine, but what I can do is rewrite that five U squared plus nine because it's in the denominator. Make it a negative. Exponents and the square root make it the one half power. And so now it's just a straight up chain rule where you have this inter function again. Look for parentheses when you do an inter function, and then the outer function is that 20 times the inter function to the negative one half power. So then when we do the derivative D R D u, you do the outer function first, where you bring this negative one half in front. Well, half of 20 is 10 making negative. And now when you subtract one from your exponents, it makes it the negative three has power. I don't know if I have to show you that work, because subtracting one is the same thing is to over to, uh, enabling minus two. His name of three halves. So that's a little thought bubble. I asked why That's the the exponents. You leave the inter function alone, and then you multiply by the derivative of the inter function. Well, the derivative of five U squared is 10 you in the derivative of 90 So we don't have to write that. Um, now you some teachers will let you leave your answer like this. Other teachers might actually ask you to, you know, simplify Negative. 10 times 10 is negative. 100. You on, then over because of the negative exponents. So that's gonna stick into the denominator. And some teachers will just let you leave it as vibe you squared. Plus nine to the positive. Three has power. Other teachers might tell you to write as the square root of five u squared plus nine cubed. But this should be good enough this or this Or, you know, there's a lot of other ways of writing the same thing in that

View More Answers From This Book

Find Another Textbook

01:11

Suppose that, in the development of the definition of the derivative, we wro…

02:28

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

02:05

Locate all critical points.$$h(x)=\frac{1}{x^{2}-x-2}$$

03:03

Let $y 1(x)=x^{2}+1,$ determine the equation of the secant line through each…

01:39

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

04:48

Plot each of the following lines on the same set of axes. (a) $y=2 x$(b)…

03:20

Suppose that $Q=x^{2} y^{-3} .$ If $d Q / d t=6$ and $d x / d t=2,$ find $d …

04:29

One of the most commonly used mathematical models for a demand function in m…

02:07

$y=\left(3 t^{2}+2 t\right)^{-1 / 2},$ find $d y / d t$.

02:06

$y=\left(5 x^{2}-7 x+2\right)^{3 / 4},$ find $d y / d x$.