   Chapter 13.2, Problem 14E

Chapter
Section
Textbook Problem

# Find the derivative of the vector function.14. r(t) = sin2at i + tebt j + cos2ct k

To determine

To find: The derivative of the vector function r(t)=sin2ati+tebtj+cos2ctk.

Explanation

Formula used:

Consider the standard formula for derivative of sint,cost, and et.

ddtsint=costddtcost=sintddtsin2at=2sinatddt(sinat)ddtet=et

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

Differentiate each component of the vector function r(t)=sin2ati+tebtj+cos2ctk as follows.

ddt[r(t)]=ddt[sin2ati+tebtj+cos2ctk]

Rewrite the expression as follows.

r(t)=ddt(sin2at)i+ddt(tebt)j+ddt(cos2ct)k

Use the following formula to compute the expression.

ddt[u(t)v(t)]=u(t)ddt[v(t)]+v(t)ddt[u(t)]

Modify equation (1) using the above formula

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