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Establish the following rules for working with differentials (where $ c $ denotes as constant and $ u $ and $ v $ are functions of $ x $).(a) $ dc = 0 $ (b) $ d(cu) = c du $(c) $ d (u + v) = du + dv $ (d) $ d(uv) = u dv + v du $(e) $ d ( \frac {u}{v}) = \frac {v du - u dv}{v^2} $ (f) $ d(x") = nx^{n-1} dx $

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Campbell University

Oregon State University

Boston College

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.

06:46

Establish the following ru…

06:40

01:34

Formulas for Differentials…

14:40

Verify that the given func…

00:08

For each function $u(x)$ i…

Hey, it's clear. So when you raid here so we have Do you see is equal to t over D acts see defense, which is equal to zero D acts which becomes equal to zero for part B. We have d over d Let's see you d x Just be cool to see do you over dx d x which is equal to see Do you for part C you have the d V plus you Yeah, de over de pecs you plus V d x which is equal to dio over d That's it's less TV over t x the nets we get Jeanne you for Psst! Let's plus TV over t x d x But you see what to do You plus de mi party get d You ve is equal to D over d x u v d x where he used the product will get you Devi over the nets us b of to you over d x x We get you Devi plus we do you her eeg We have t of you over b Jesse called de over de acts you over v the X Mexico to me Do you over t X minus you Devi over D cups over the square T x which is equal to ve to you on us You devi over the square for F We have a team of extreme and power is equal to de over de Metz of X to the end Power Tietz we get then next the n minus one power dance.

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