For each of the following functions, find the derivative vector for those points where it is defined:
a. I know that . As a result, then
By taking the partial derivatives, then
So, the gradient would be
However, I have a hard time understanding the gradient vector/derivative vector. I'm slightly confused because I thought was called the gradient and not a vector. If I can just understand this, then I can do (c) as well.
Thank you for your time.
You can remember the definition of del.
(that is the standart basis of the space)
So as you see here, del is taken as a vector.
Now we can derive the operators (for ).
Let be a scalar function.
What we did here was multiplying a vector (del) by a scalar (f).
Let F be a vector function such that .
We just applied dot product here.