Please provide step my step instructions:

Define f : R³ R² by f(x,y,z) = (x ²y + zx cos(z), e^{x+y sin(z)} ). Compute the Jacobian matrix of f at an arbitrary point (x,y,z) in R³

and

Step by step for this one:

When looking at economics, Cobb-Douglas functions can be used to model how a company's production amount (P) depends on the amount of labor involved (L) and the amount of capital invested (K). For a particular company, this relationship can be modeled the following:

P(L, K) = L^2/3K^1/3

(1) The company that currently has L = 8 and K = 1 is considering decreasing L by 0.1 and increasing K by 0.07. Use linear approximation to decide whether this would increase or decrease production and by how much.

(2) How can I use a calculator to compare the actual value of P(7.9, 1.07) with the approximation I found in the above problem (1). How accurate is this approximation?

(3) Find the linearization A(L, K) of the production function P(L, K) at (L, K) = (8, 1).

(4) Can you include a screenshot of a 3D graphing calculator to graph P together with the linearization A you found in the above problem (3).

which graphing calculator are you using is it Georgebra( so I can learn by trying this)