Phantom L.

asked • 03/24/18# Differential Equation Problem. No clue how to do this.

Find the derivatives of each of the following vectors.

x(t) = [ t

^{3}- 2t^{2}+t e

^{t}sin(t) ]
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## 1 Expert Answer

Arturo O. answered • 03/24/18

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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) = (t

^{3}- 2t

^{2}+ t)

**i**+ e

^{t}sin(t)

**j**

d

**x**/dt = (3t^{2}- 4t + 1)**i**+ [e^{t}sin(t) + e^{t}cos(t)]**j**Again, this is valid only if the unit vectors

**i**and**j**are constant.Phantom L.

How would I know if vectors "i" and "j" are constants?

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03/24/18

Phantom L.

How would I know that "i" and "j" are constant? And to re-write it in a vector function form from a bracket form, do I just simply take the top equation which would be my "i", combining with my 2nd equation would be my "j"?

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03/24/18

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Arturo O.

_{1}(t) = t^{3}- 2t^{2}+ t_{2}(t) = e^{t}sin(t)03/24/18