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

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Campbell University

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

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