I know that:
$$ \nabla(a\cdot b) = (a\cdot\nabla)b +(b\cdot \nabla)a + a\times(\nabla\times b)+ b\times (\nabla \times a) $$
and also that:
$$ \nabla(a\cdot b) = (\nabla a)\cdot b + (\nabla b)\cdot a $$
With this in mind I want to find the "simplest" expression for $\nabla(a\cdot a)$ other that $$ \nabla(a\cdot a) = 2(\nabla a)\cdot a $$ I need to avoid the use of matrices ($\nabla a$).
Thanks in advance...