Abstract

This chapter elaborates the vectors and derivative of a product. It is assumed that the vector r is a continuous single-valued function of the scalar variable t. When t increases by a small scalar quantity δt, r increases by a small vector quantity δr. The derivative of r with respect to t is defined. The derivative of r, when it exists, is in general also a function of t, and if dr/dt is differentiable its derivative is the second derivative of r with respect to t and is written d2r/dt2. The derivative of a product of two functions, at least one of which is a vector, is formed in the same way as the derivative of a product of two scalar functions, with the restriction that, in the case of the vector product of two vectors, the order of the two functions, r1 and r2 must remain unaltered.

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