   Chapter 12.2, Problem 16E

Chapter
Section
Textbook Problem

# Finding a Derivative In Exercises 11-18, find r ' ( t ) . r ( t ) = 4 t i + t 2 t j + ln t 3 k

To determine

To calculate: The derivative of the function r(t)=4ti+t2tj+lnt2k.

Explanation

Given:

The vector-valued function r(t)=4ti+t2tj+lnt2k.

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)=4ti+t2tj+lnt2k=4t1/2i+t5/2j+2lntk

Differentiate the function with respect to t and obtain the following result:

r(t)=ddt(

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