e^x Calculator

Understanding e^x (Exponential Function)

What is e^x?

e^x, also known as the exponential function, is a mathematical function where the constant e (Euler's number, approximately 2.71828) is raised to the power of x. It's one of the most important functions in mathematics, with applications in various fields including physics, engineering, and finance.

Mathematical Definition

The exponential function e^x is defined as:

\[f(x) = e^x\]

Where:

• e ≈ 2.71828 (Euler's number)
• x is any real number

Properties of e^x

1. e^0 = 1
2. e^1 = e
3. The derivative of e^x is itself: \(\frac{d}{dx}e^x = e^x\)
4. It's always positive for real x: e^x > 0 for all x
5. It's its own inverse: ln(e^x) = x

Calculation Steps

To calculate e^x:

1. Identify the value of x
2. Use the formula: y = e^x
3. Substitute the value of x and calculate
4. Round to the desired number of decimal places

Example with Visual Representation

Let's calculate e^2:

1. x = 2
2. y = e^2
3. y ≈ 7.3890560989
4. Rounded to 4 decimal places: y ≈ 7.3891

This graph shows the exponential function e^x. The red point represents e^2 ≈ 7.3891.