Derivatives of vector-valued functions Differentiate the following function. r(t)=\langle4,\ 3\cos 2t,\

Halkadvalseln

Halkadvalseln

Answered question

2021-11-26

Derivatives of vector-valued functions
Differentiate the following function.
r(t)=4, 3cos2t, 2sin3t

Answer & Explanation

Mary Ramirez

Mary Ramirez

Beginner2021-11-27Added 19 answers

Step 1
The given function is:
r(t)=4, 3cos(2t), wsin(3t)
We have to differentiate the given function.
The given function can be written as:
r(t)=4i+3cos(2t)j+2sin(3t)k
Step 2
Therefore we have r(t)=4i+3cos(2t)j+2sin(3t)k
Now differentiate both the sides with respect to t.
Therefore,
d(r(t))dt=d(4i+3cos(2t)j+2sin(3t)k)dt
=d4dti+d3cos(2t)dtj+d2sin(3t)dtk
=0i+3dcos(2t)dtj+2dsin(3t)dtk
=3(sin(2t))d2tdtj+2(cos(3t))d3tdtk
=3sin(2t)×2j+2cos(3t)×3k
=6sin(2t)j+6cos(3t)k
Step 3
Therefore,
d(r(t))dt=6sin(2t)j+6cos(3t)k

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