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Numerade Educator



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 $


(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) $\left(n x^{n-1}\right) d x$


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Video Transcript

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