   Chapter 12.2, Problem 23E

Chapter
Section
Textbook Problem

# Higher-Order DifferentiationIn Exercises 19–22, find (a) r ′ ( t ) , (b) r ″ ( t ) , and (c) r ′ ( t ) ⋅ r ″ ( t ) . r ( t ) = 4 cos t i + 4 sin t j

(a)

To determine

To calculate: The derivative r'(t) for the provided function r(t)=(4cost)i+(4sint)j.

Explanation

Given:

The provided function is r(t)=(4cost)i+(4sint)j.

Formula used:

The differentiation of the function sinx and cosx is:

ddx(cosx)=sinxddx(sinx)=cosx

Calculation:

Consider the function r(t)=(4cost)i+(4sint)j

(b)

To determine

To calculate: The Second derivative r''(t) for the provided function r(t)=(4cost)i+(4sint)j.

(c)

To determine

To calculate: The dot product r'(t)r''(t) for the provided function r(t)=(4cost)i+(4sint)j.

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