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Problem

Find the derivative of the function. Simplify whe…

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Problem 59 Hard Difficulty

Find the derivative of the function. Simplify where possible.
$ y = \arccos ( \frac {b + a \cos x}{a + b \cos x}), 0 \le x \le \pi, a > b > 0 $


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01:22

Frank Lin

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Related Topics

Derivatives

Differentiation

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Video Thumbnail

04:40

Derivatives - Intro

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.

Video Thumbnail

44:57

Differentiation Rules - Overview

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.

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Video Transcript

this from Where's fund dirigible coastline immerse Be off B plus acres on X, divided by eight people's connects him. You know that they were focused on your stuff or negative order was scared. Apartments and sperm. So then we have my front as native born forward skirt off. Born minus B plus acre Sine X, divided by a plus B Cups. I next squared months fly by director to DDX off speed plus a co sign X You want a plus B coaster X for we can write. Why prime as negative one Over are screwed off a plus. Speak of sign of X squared minus B plus a co sign of X squared divided by a plus B co signer. X squared. There's all in sperm, most like by Derek talk dysfunction. So we're gonna use caution rule. And that uses negative a sign. Next time's a plus B co signer X minus B plus, eh? No sign of eggs. Classmates to be of sine x. You got it. Bye. It must be co signer Pegs squared. No, you can't do right by point s. Now let's take this guy. And don't forget, this is Wilson's spirit. So Let's take this one and write it and numerator And then let's get rid of Spirit Route. Since we have harbored do right here, we can't let that one has negative off a plus B Co sign of X. You ride it by spurred Oh, a squared. So I'm expanding these two terms base Where plus two A B co signer fights WASPy Spirit Co signed spirit of X minus Be spread minds to a B no sign of X minus a spread. Co signed X Now to a because I'm effects, these terms will cancel out off For this term. We have negative A spread scientifics minus a B sign. Eggs have Sinus plus B squared sine X plus a be co sign X Inside X, divided by eight plus be co sign X squared now a B science coastline. Next terms for kids out. Also, we can see by this We have papers. People said it's here. We have skirt got here so we'll have a party for sonnets and dino man right here so we can burn the right time as signings Times base worried. Less peace word divided by oh, we have screwed off base. Birdman's peace word waas co sign squared effects planes. Uh, this is minus based graybeards be scraped here. That is incense bird demanded by skirt A plus B comes on X Now we have a scrape My mind's be strict term here in here so we can turn it out Let's write the this one on a science Eggs times ace grade money He's where? Divided by scribe Oh, a scribe Minutes be spread Well, Spike five spirit good off your mind school science for have you know that one? Let's go Sense spirit of ecstasy with science Cardiff, Lex and screwed up Science part of X will be sign of eggs and side effects is working out We have been almost not for that this term. We also have one or a speaker sign of banks. Now we have a scribe minds be spirit Here in the numerator You also have spirit of backing denominated So we can just let out a little time skirted off a spread months be skirting the numerator What I'm the answer will be described it off a spirit friend speech Berg united by a plus. He co signed X

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Related Topics

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Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Catherine Ross

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Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

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.

Video Thumbnail

44:57

Differentiation Rules - Overview

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.

Join Course
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