   Chapter 12.2, Problem 72E

Chapter
Section
Textbook Problem

# ProofIn Exercises 61–68, prove the property. In each case, assume r , u , and v are differentiable vector-valued functions of t in space, w is a differentiable real-valued function of t , and c is a scalar. d d t [ r ( t ) × r ′ ( t ) ] = r ( t ) × r ″ ( t )

To determine

To prove: The expression ddt[r(t)×r'(t)]=r(t)×r''(t)

Explanation

Given:

Assume, r, u, and v are differentiable vector-valued functions of t in space, w is a differentiable real-valued function of t and c is a scalar.

Formula used:

The derivative formula is:

ddt[r(t)×u(t)]=r(t)×u'(t)+r'(t)×u(t)

Proof:

Consider the function,

ddt[r(t)×u(t)]=r(t)×u'(t)+r'(t)×u(t)

ddt[r(t)×

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