If u(x) = f (x) + it(x) is a complex-valued function of a real variable x and

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If u(x) = f (x) + it(x) is a complex-valued function of a real variable x and the real and imaginary parts f (x) and g(x) are differentiable functions of x, then the derivative of u is defined to be u'(x) = f'(x) + ig'(x). Use this together with Equation 7 to prove that if F(x) = erx, then F'(x) = rerx when r = a + bi is a complex number.

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