calculate the jacobian matrix for the given function at the indicated point. write a formula for the total derivative.
H(r, theta)= (rcostheta, rsintheta) a= (square root of 2, 3pi/2)
so i changed it to H(x,y) and got the matrix
1 0
0 1
but the answer in the back of the book is
0 squ.rt 2
-1 0
i feel like it has to do with the point a but i don't know where i'm supposed to plug this point in? or how to write the formula for the total derivative?
sorry this is my first time doing derivatives in this class so i'm a bit confused
By total derivative are you talking about the total differential?
By total derivative we can also mean the derivative of a function of several variables with respect to one of the input variables.
Both formulas are in the attachment
If you are talking about the Total Derivative of a Transformation if I am not mistaken that is the Jacobian matrix.
I would like some clarification on that myself. My best guess is based on what I know of differentials for single valued functions is detJ * drd(theta) = rdrd(theta) (areal element for polar coords)