Question: The exponential function f(x) = e has the remarkable property that it's equal to its own derivative. So does the constant function f(x) =

The exponential function f(x) = e has the remarkable property that it's

The exponential function f(x) = e has the remarkable property that it's equal to its own derivative. So does the constant function f(x) = 0. Are there any other functions with this property? If so, can you describe them all? Hint: Suppose f(x) and g(x) each have the property that they're equal to their own derivatives. Then consider the derivative of the quotient f(x)/g(x).

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