http://calc3.askbot.com/questions/Open source question and answer forum written in Python and DjangoenCopyright Askbot, 2010-2011.Wed, 16 Jul 2014 20:56:18 -0500http://calc3.askbot.com/question/108/gradient-of-fxy/So I feel like I should know this but... In three dimensional space the del operator is defined as $\nabla =\langle \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z} \rangle$. So when dealing with a function like the one in problem 4 of the review sheet; $f(x,y)=xy^{3}$. Do we treat del as being $\nabla=\langle \frac{\partial}{\partial x}, \frac{\partial}{\partial y} \rangle$ and find a gradient with two components or do we remake the function into a level surface such as $xy^{3}-z=k $ where $k \in \mathbb{Z} $ and find a gradient with three components? If this is obvious I'm incredibly sorry but it really is bugging me.Wed, 16 Jul 2014 20:36:25 -0500http://calc3.askbot.com/question/108/gradient-of-fxy/http://calc3.askbot.com/question/108/gradient-of-fxy/?answer=110#post-id-110The gradient of a function of $n$ variables is an $n$-dimensional vector.Wed, 16 Jul 2014 20:56:18 -0500http://calc3.askbot.com/question/108/gradient-of-fxy/?answer=110#post-id-110