Download the App!

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

Find the derivative of the function

$ F(x) = \frac {x^2 - 5x^3 + \sqrt{x}}{x^2} $

in two ways: by using the Quotient Rule and by simplifying tirst. Show that >our an\uer\ are equivalent Which method do you prefer?

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

See solution for details

01:51

Frank Lin

02:38

Clarissa Noh

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Ryan R.

October 6, 2021

I think you copied the problem wrong.

Campbell University

Baylor University

University of Nottingham

Idaho State 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.

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.

07:48

Find the derivative of the…

04:13

13:48

03:09

Find the derivative of: f…

01:02

Find the indicated derivat…

01:31

$$\text { } , \text { …

08:35

Find the derivative of $f(…

02:08

Find each indicated deriva…

04:29

Compute the indicated deri…

00:29

All right, We've got a question here. Function of votes equal to X squared my five x, you plus the square root of X all divided by X work. Mhm. All right. And we are asked to find the derivative in two ways by using the quoting rule and by simplifying first. All right. Now, start off by using a quota rule, which is where we take the derivative of the numerator multiplied by the denominator. Basically, you take a square. Do you do X? The numerator multiplied by the denominator. Subtracting the derivative, the derivative of the A derivative of the denominator multiplied by the new All of that divided by the numerous. The denominator street. Okay, so the quote and rule states that if you take the derivative, the denominator multiplied. She's a derivative of the numerator, multiplied by the denominator, subtracting the derivative of the denominator multiplied by the numerator, all divided by denominated squared. You can get the first derivative of your function. You have X squared multiplied by two X minus 15 x squared, plus squirrels of extra riveted. It's the same thing. One over one. Over two, one over to root books. Uh, X squared minus five x cubed. Yeah. And then Drew. Experts sentence to acts all over X before have you got right? And then we'll get a two x cubed minus 30 ext four. It looks like there's a bit of a typo here. This is actually supposed to be extra for. So then this would be more X to the vote. All right, so then when we go ahead and simplify all of this, we will get two extra there minus five X fourth, minus three halves X would X all over extra. Fourth. We've simplified that will get two x five minus three. Uh huh. Excuse the negative five. That will be our final answer when we try to take the derivative using the quoting rule. And then if we use the who tried to take the derivative after a simplification, Basically, what we're doing is we're taking our equation x to the fourth minus five X cubed on his actual X over X squared. Getting you simplify, it will get X squared minus five x minus A. Excuse me was This should be a process. We have a plus a x to the negative. Excellent. Negative three half And then when you take the derivative of this, we'll have to X minus five was minus a. We have X, the negative five. All right, we can see that this was actually a lot simpler to do. There's gonna be situations where it's not easy to simplify, so you're going to use the court to rule and you'll you'll be able to get your answer. But in this specific situation, you can see that it's a lot easier if we had just simplified. All right, well, I hope that clarifies the question there. Thank you so much for watching.

View More Answers From This Book

Find Another Textbook