Differentiate the vector-valued function r(t)=<<\sin(t^2),4t^2-t>> .

Coroware

Coroware

Answered question

2021-11-30

Differentiate the vector-valued function r(t)=sin(t2),4t2t.

Answer & Explanation

John Timms

John Timms

Beginner2021-12-01Added 8 answers

Step 1
Given r(t)=sin(t2),4t2t.
Step 2
We find derivative of components "w.r.t" to "t"
ie ddt=cos(t2)ddt(t2)
=cos(t2)2taskPSKddt(tn)=ntn1
ddt(4t2t)=ddt(4t2)ddt(t)
=4ddt(t2)1
=8t1
Hence
r(t)=2tcos(t2),8t1

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