Let u = f(x) and v = g(x) be differentiable mappings from a domain D in 3−dimensional space to 3−dimensional space. Let aand bbe constant scalars. Let A be a constant 3 × 3 matrix. Show:
a) d(u + v) = du + dv
b) d(au + bv) = adu + bdv
c) d(Au) = Adu
d)d(u • v) = u • dv + v • du
e)(u × v) = u × dv + du × v
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