(I am not very sure if this is a high-school level question or a undergraduate level question. Sorry.)(adsbygoogle = window.adsbygoogle || []).push({});

Does our normal differentiation rules, like the product rule and quotient rule apply to vectors?

Say for example, differentiate ##r \times \dot r##

##r## is radius vector, ##\dot r## is the time derivative of the radius vector (i.e. velocity vector), and you cross both vector (thus the product is a vector, not a scalar as in dot multiplication.)

Now in normal case, assume that ##r## and ## \dot r## are both scalar, not vector, we will apply product rule, i.e. differentiate the first variable (##r##), retain the second (##r##), multiply both, plus differentiate the second variable (##r##) and add with the first variable (##r##)

So, your result is:

(##r \times \ddot r ##) + (## \dot r \times \dot r##)

But what about vectors? If both ##r## and ## \dot r## are vectors and you cross multiply or dot multiply them, will you differentiate them the same way like you do as if they were scalars?

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# I Do normal differentiation rules apply to vectors?

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