The natural exponential function is defined as the function $$f(x) = e^x$$, where $$e$$ is an irrational constant approximately equal to 2.71828. This function is significant because it serves as the base for natural logarithms and is widely used in calculus, especially in growth and decay problems. Its unique property is that the derivative of the function is equal to the function itself, making it a key player in differential equations and many areas of applied mathematics.
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