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
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Identify the function and the rule to apply
We need to find the derivative of the function $e^x$, known as the exponential function.
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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.
$$\frac{d}{dx} e^x = e^x$$
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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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