Differential Equation Problem. No clue how to do this.

Question

Find the derivatives of each of the following vectors.

 

x(t) = [ t³ - 2t² +t

                e^tsin(t) ]

Answer 1

You can differentiate each component as long as the unit vectors are not time-dependent.  For fixed unit vectors i and j, it looks like your vector function is

 

x(t) = (t³ - 2t² + t)i + e^tsin(t)j

 

dx/dt = (3t² - 4t + 1)i + [e^tsin(t) + e^tcos(t)]j

 

Again, this is valid only if the unit vectors i and j are constant.