Derivatives of vector-valued functions Differentiate the following function. r(t) = <4,

osteoblogda

osteoblogda

Answered question

2021-12-06

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

Answer & Explanation

soanooooo40

soanooooo40

Beginner2021-12-07Added 35 answers

Step 1
the given function is:
r(t)=<4,3cos(2t),2sin(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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