The function for which first derivative is itself is "e^x". This function is the solution of the equation "y'=y", since it is given that the first derivative is itself. Hence option (A) is the correct option.
The function for which first derivative is constant multiple of "k" of itself is "e^{kx}" . This function is the solution of the equation "y'=ky", since it is given that the first derivative is a constant multiple of "k" to itself. Hence option (D) is the correct option.
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