How do i prove that a = v * dv/dx?

my book says that a =dv/dt = dv/dx * dx/dt = dv/dx * v

that looks all ok but according to this equation it seems that x(displacement) is a function of t whereas x=v * t. so how can we differentiate x without differentiating v which leads to circular reasoning?

What should the power status of a circuit be when measuring resistance with an ohmmeter?

An architect plans to use solar energy to heat the next house he designs. what principle of absorption and infrared energy can be applied to the design of the new house? how could she apply to those principals?

Aspecified volume of space contains an electric field for which the magnitude is given by e=e0cos(ωt). suppose that e0 = 20 v/m and ω = 1.0 × 107 s−1. part a what is the maximum displacement current through a 0.80 m2 cross-sectional area of this volume? express your answer with the appropriate units. idisp,max i d i s p , m a x = nothing nothing request answer part b how would this area have to be oriented relative to the electric field to get this maximum displacement current?