   Chapter 13.2, Problem 16E

Chapter
Section
Textbook Problem

# Find the derivative of the vector function.16. r(t) = t a × (b + t c)

To determine

To find: The derivative of the vector function r(t)=ta×(b+t)c.

Explanation

To find the derivative of the vector function, differentiate each component of the vector function.

Differentiate each component of the vector function r(t)=ta×(b+t)c as follows.

ddt[r(t)]=ddt[ta×(b+t)c]

Rewrite and compute the expression as follows.

r(t)=ddt[t(a×b)+t2(a×c)]=ddt[t(a×b)]+ddt[t2(a×c)]=(ax

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