What is the derivative of e^x?

The derivative of the function e^x is indeed e^x. This is a fundamental result in calculus, known for the unique property of the exponential function with base e. The function e^x is special because it is its own derivative, meaning that when you differentiate it with respect to x, you simply get the same function back.

This property is a key reason why e is often used in mathematical modeling, particularly in growth and decay problems, as it simplifies many calculations involving continuous change. Other functions involving exponential or logarithmic relationships do not share this property, making e^x unique in its behavior.