We define the partial derivative of a vector valued function f = (f1, f2, …, fn) by (a) Wi...

We define the partial derivative of a vector valued function f = (f1, f2, …, fn) by

(a) With f(x, y) = (x3 − 3xy2, 3x2y − y3), calculate and .

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(b) Figure 1 shows several values of f. Use f(0.75, 0.5), f(1, .5), and f(0.75, 1) to approximate and . Compare these with the exact values of the partials at this point.

Figure 1