   Chapter 13.2, Problem 12E

Chapter
Section
Textbook Problem

# Find the derivative of the vector function.12.  r ( t )  =  1 1  +  t i  + ​   t 1 + t j +  t 2 1  +  t k

To determine

To find: The derivative of the vector function r(t)=11+ti+t1+tj+t21+tk.

Explanation

Formula used:

The formulas that are used is,

ddt(1t)=(1t2)ddt(11+t)=1(1+t)2ddt[u(t)v(t)]=v(t)ddt[u(t)]u(t)ddt[v(t)]v2(t)

Calculation:

To find the derivative of the vector function, differentiate each component of the vector function r(t)=11+ti+t1+tj+t21+tk as follows.

ddt[r(t)]=ddt[11+ti+t1+tj+t21+tk]

Rewrite the expression as follows.

r(t)=ddt(11+t)i+ddt(t1+t)j+ddt(t21+t)k

Compute the expression r(t)=ddt(11+t)i+ddt(t1+t)j+ddt(t21+t)k by using above mentioned formulae as follows

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