💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Numerade Educator

Like

Report

Problem 41 Hard Difficulty

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 $

Answer

(a) 0
(b) $c d u$
(c) $d u+d v$
(d) $u d v+v d u$
(e) $\frac{v d u-u d v}{v^{2}}$
(f) $\left(n x^{n-1}\right) d x$

Discussion

You must be signed in to discuss.

Video Transcript

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.