How is the differentiation of a vector sum performed?

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SUMMARY

The differentiation of a vector sum follows the same principles as scalar functions. Specifically, the derivative of a vector sum, expressed as d/dt (u + t), is calculated using the linearity of differentiation, resulting in (u + t)' = u' + t'. This confirms that each component of the vector can be differentiated independently and summed. The discussion clarifies that the differentiation process does not require any additional steps beyond applying the linearity rule.

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FOIWATER
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I know how to differentiate the dot and cross products of two vectors, is the differentiation of a vector sum done like this:

d/dt (u+t) = u' + t + u + t'

Or simply add them and then differentiate?

Thanks
 
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(u+t)'=u'+t', as it is for scalar functions. This is linearity.
 
thanks
 

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