   Chapter 13.2, Problem 11E

Chapter
Section
Textbook Problem

# Find the derivative of the vector function.11. r(t) = t2i + cos(t2)j + sin2t k

To determine

To find: The derivative of the vector function r(t)=t2i+cos(t2)j+sin2tk.

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)=t2i+cos(t2)j+sin2tk as follows:

ddt[r(t)]=ddt[t2i+cos(t2)j+sin2tk]

Rewrite the expression as follows:

r(t)=2ti+ddt[cos(t2)]j+ddt(sin2t)k

Use the following formula to compute the expression:

ddtcost=sintddtcos(t2)=(2t)sin(t2)ddtsin2(t)=2<

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