Use the chain rule cos sin second derivative cos

Derivatives of vector function Assignment Answers Needed

Your Question:

$(t)' = [-6 sin(2t), 6 cos(2t), 4]$

This can be found by differentiating each of the three components of the vector function. For example, to differentiate the first component, we use the chain rule:

d/dt [-6 sin(2t)] = -12 cos(2t)

Therefore, the first and second derivatives of (t)=[3cos(2t),3sin(2t),4t] are: