I'm reading through a section of Alan Jeffery's book Mathematics for Engineers and Scientists. In particular the derivative of a vector function, the context of the analysis is a position vector of a point $\mathbf{u}(t)$ which is a function of $t$ (say, time) that moves along a given curve.
The section of the book proves/shows that the the instantaneous speed (i.e the scalar rate of change of distance along the curve) is the magnitude of the the vector $\mathrm{d}\mathbf{u}/\mathrm{d}t$.
I follow the analysis up until equation eqn (11.5) I can't understand how that equation is obtained from the preceding one (which un-numbered).
Other online notes arrive at the same result without equation 11.5. Could some explain how eqn 11.5 on page 2 is obtained from the immediately preceding line.
Some of the questions I've seen are humblingly rarefied, so apologize for my simple one !