Question

what exactly do we find a gradient for and how do you find the gradient of a function?

Answer 1

the gradient of a function is the vector whos components are the partial derivatives of the function.

ex. \[f(x,y)=x ^{2}+y ^{2}\]
then the gradient del f=2xi+2yi

Answer 2

makes sense. My only question is why we only look at the function in the i direction and not the j or k? How do you know which one to choose?