What is ?
If we consider the domains of and of as consisting of column vectors, then can be written as a multiplication by a matrix. What is this matrix?
There are 6 partial derivatives of . Evaluate .
The gradient of at the point of can also be thought of as a linear map into . What is the corresponding matrix?
Now is a function from to with a gradient represented by a matrix. Writing for , what is this matrix at the point ?
Write a matrix equation relating with .
List the partials , and .
In terms of , and , write an expression for .
The function can be considered in terms of the polar coordinates via the transformation where and . By considering as the second component of , or otherwise, write an expression for this partial derivative in terms of and .