Please show all working. For a vector-valued function in the plane, write the ta

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Please show all working.

For a vector-valued function in the plane, write the tangent vector as a column vector, or 2 times 1-matrix. by defining the Jacobi matrix Similarly, for a function of two variables define the Jacobi matrix Df as the 1 times 2 matrix of partial derivatives of z = f(x, y): For the curve r(t) in R2. and function f on R2 defined by r(t) = (cost, sin t), f(x, y) = x2 - 2y2, calculate an expression for the composite function p(t) = f o r(t) as a function of 1-variable t. Calculate Df, Dr, and Hence verify directly that, as a 1 times 1 matrix, obtained by multiplication of Jacobi matrices.

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