What is the derivative of e to the x?

Understand the Problem

The question is asking for the derivative of the function e^x. Since e^x is a well-known function in calculus, its derivative is straightforward and does not require extensive calculations.

Answer

e^x
Answer for screen readers

The derivative of the function e^x is e^x

Steps to Solve

  1. Identify the function and the rule to apply

    We need to find the derivative of the function $e^x$, known as the exponential function.

  2. Apply the exponential rule

    One of the fundamental rules in calculus for derivatives is that the derivative of $e^x$ with respect to $x$ is $e^x$ itself.

    $$\frac{d}{dx} e^x = e^x$$

  3. Write the result

    Therefore, the derivative of the function $e^x$ is simply $e^x$.

The derivative of the function e^x is e^x

More Information

The exponential function $e^x$ is unique in calculus because its rate of change is directly proportional to its value. This property makes it a fundamental function in mathematics and has applications in various fields, including science and engineering.

Tips

Don't confuse the function $e^x$ with other exponential functions such as $a^x$ where $a$ is a constant other than $e$. The derivative of $a^x$ is not as straightforward and involves a natural logarithm.

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