   Chapter 12.2, Problem 13E

Chapter
Section
Textbook Problem

# Finding a Derivative In Exercises 9–20, find r'(t). r ( t ) = 6 t i − 7 t 2 j + t 3 k

To determine

To calculate: The derivative of the vector-valued function r(t)=6ti7t2j+t3k.

Explanation

Given:

The vector-valued function r(t)=6ti7t2j+t3k.

Formula used:

For a vector-valued function r(t)=f(t)i+g(t)j+h(t)k where f, g and h are differentiable functions of t, the derivative of the function is given by,

r(t)=f(t)i+g(t)j+h(t)k

Calculation:

Consider the provided vector-valued function,

r(t)=6ti7t2j+t3k

Here, the components of the function f(t)=6t and g(t)=7t2 and h(t)=t3 are polynomial functions and hence differentiable everywhere

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