The gradient is just the jacobian matrix correct

$\displaystyle f(x,y) = \log \sqrt{x^2 + y^2}$

$\displaystyle \nabla f(x,y) = \left[\begin{array}{cc} \frac{1}{\ln 10}\frac{x}{x^2+y^2}&\frac{1}{\ln 10} \frac{y}{x^2 +y^2} \end{array}\right] $ ??

also, I went to a couple differential geometry talks before and they were referring to nabla notation, were they referring to the gradient?