Chapter 2.9, Problem 39E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Establish the following rules for working with differentials (where *c* denotes a constant and *u* and *v* are functions of *x).*

(a)

(b)

(c)

(d)

(e)

(f)

To determine

**To establish:**

The given rules using differentials.

Explanation

**Concept:**

If a function y = f(x) then dy and dx are differentials and relation between them is,

dy = fâ€™(x) dx

**Calculation:**

We shall verify each of the given statements.

**(a)**

By using differentials,

Thus,

**(b)**

By using differentials,

By using constant multiple rule,

Thus,

**(c)**

By using differentials,

By using sum rule,

Thus,

**(d)**

By using differentials,

By using product rule,

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