   Chapter 12.2, Problem 21E

Chapter
Section
Textbook Problem

# Higher-Order Differentiation In Exercises 19-22, find (a) r ' ( t ) , (b) r " ( t ) , and (c) r ' ( t ) ⋅ r " ( t ) . r ( t ) = t 3 i + 1 2 t 2 j

(a)

To determine

To calculate: The first derivative of the function r(t)=t3i+12t2j.

Explanation

Given:

The vector-valued function r(t)=t3i+12t2j.

Formula used:

If r(x)=f(x)ig(x)j, where f and g are the differentiable functions of x, then

r(x)=f(x)ig(x)j

Calculation:

Consider the function:

r(t)=t3

(b)

To determine

To calculate: The second derivative of the function r(t)=t3i+12t2j.

(c)

To determine

To calculate: The dot product of the first derivative and second derivative of the function r(t)=t3i+12t2j.

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