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Chapter 4: Problem 78

What is the natural exponential function?

Short Answer

Expert verified
The natural exponential function is expressed as \( e^x \), where \( e \) is the Euler's number. It exhibits properties like being its own derivative, always positive and increasing, and able to multiply similar base exponentials together.

Step by step solution

01

Definition

The natural exponential function is denoted as \( e^x \), where \( e \) is Euler's number, approximately equal to 2.71828. This function is defined for all real numbers, and it's always positive.
02

Properties

Some remarkable properties of natural exponential functions include derivative and integral of \( e^x \) is \( e^x \) itself, \( e^x \) is always increasing and never equals to zero. Moreover, the sum of exponents allows similar base exponentials to multiply together, i.e., \( e^{x}*e^{y} = e^{x+y} \).

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can solve \(4^{x}=15\) by writing the equation in logarithmic form.

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