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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 $

(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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Campbell University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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