Chapter 12, Problem 19RE

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
1 views

# Higher-Order Differentiation In Exercises 19 and 20, find (a)r’(t),(b)r”(t) and (c) r'(t) r"(t). r ( t ) = ( t 2 + 4 t ) i − 3 t 2 j

(a)

To determine

To calculate: The first derivative of the function r(t)=(t2+4t)i3t2j.

Explanation

Given:

The vector-valued function is: r(t)=(t2+4t)i3t2j.

Formula used:

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

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

Calculation:

Consider the provided function,

r(t)=

(b)

To determine

To calculate: The second derivative of the function r(t)=(t2+4t)i3t2j.

(c)

To determine

To calculate: The dot product of the first derivative and second derivative of the provided function r(t)=(t2+4t)i3t2j.

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