If A(t) is a 2 2 matrix of differentiable functions and X(t) is a 2

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If A(t) is a 2 × 2 matrix of differentiable functions and X(t) is a 2 × 1 column matrix of differentiable functions, prove the product rule

[A(t)X(t)] = A(1)X'(t) + A'(t)X(t). dt

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