Chapter 6.12, Problem 3MP

The force on a charge $q$ moving with velocity $v=dr/dt$ in a magnetic field $B$ is $F=q(v\times B).$ We can write $B$ as $B=\nabla \times A$ where $A$ (called the vector potential) is a vector function of x, y, z, t. If the position vector $r=ix+jy+kz$ of the charge $q$ is a function of timet, show that $\frac{dA}{dt}=\frac{\partial A}{\partial t}+v\cdot \nabla A$

Thus show that