e Calculator | eˣ | e Raised to Power of x
Are you solving an equation with Euler's number? Our e calculator is here to help! Our tool allows you to compute e to the power of any number you desire.
Keep on reading if you're still wondering what exactly Euler's number is, what does e mean on a calculator, and how to calculate e to the x 📐🧑🏫
🙋 You can also explore the exponential functions of other bases with our exponent calculator.
What is e on a calculator? – e to the x
e is one of the most important constants in mathematics. We cannot write e as a fraction with integer numerator and denominator, and its decimal expansion is infinite and non-periodic – just like the famous number π. Its value is equal to 2.7182818284590452353602… and counting! (This is where rounding and approximation become essential.) 🧮
Now that we know what e (also known as Euler's number) and its approximate value is, we can start thinking about its possible applications.
e is the base of the natural logarithm, the same you can find using natural log calculator.
We use e in the natural exponential function (eˣ = e power x).
In the eˣ function, the slope of the tangent line to any point on the graph is equal to its y-coordinate at that point.
(1 + 1/n)ⁿ is the sequence that we use to estimate the value of e. The sequence gets closer to e the larger n is. When n = infinity, the sequence value is equal to Euler's number.
We use this equation in compound interest calculations.
e is equal to the result of the following factorial sum:
- e is also a part of the most beautiful equation in mathematics: 🌺
Since we already know what's the Euler's number, how about some other numbers we use in physics?
- Biot number;
- Knudsen number;
- Avogadro's number;
- Reynolds number; and
- f-number 😀
🔎 To see the real-life applications of exponential functions, head to Omni's exponential growth calculator.
How to put e in a calculator? Calculate e to the x
Since we're forced to use an approximation of e, we can simply input the value of e into any calculator.
How does it work in practice? How to calculate e to the power x?
If your calculator doesn't allow symbols, simply enter 2.718281828 (or any rounded form of this number) into your choice value box 👍
e calculator – examples
In this section, we'll answer the very big question: "How to calculate e to the power eˣ?" using both our calculator and the traditional formula.
The e calculator – it's so simple it doesn't need further explanation. Enter the value of x into the text box and enjoy your results displayed alongside the step-by-step solution 👣
The traditional calculation requires you to choose how many decimal places of the Euler's number you will use.
We decided to use 9 decimal places.
Let's follow an example:
We know that the area up to any x-value is also equal to eˣ:
We'd love to calculate the area up to the e¹⁰ function.
e¹⁰ = 2.718281828¹⁰;
2.718281828¹⁰ = 2.718281828 × 2.718281828 × 2.718281828 × …;
2.718281828¹⁰ = 22026.47.
And this is how to calculate e to the power of 10.
As you can see, calculating e to the power of x might be pretty troublesome and time-consuming – our tool is a simple solution for that unnecessary problem 🤗
What does exp mean?
"Exp" is short for "exponential" and is used in the notation exp(x) as another way to write eˣ.
How do you calculate e to the power x without calculator?
You can use the following Taylor series approximation: eˣ = 1 + x + x²/2! + x³/3! + …. Continue calculating and adding terms to get a better approximation.
What is e to the negative infinity?
Zero. Let's say we have e-N, where N is a large number tending toward infinity. Now, given that e-N = 1/eN, as N gets larger, e-N will get smaller, ending up at zero if N = ∞.
What is the derivative of e to the x?
The derivative of eˣ is itself, eˣ. Here is a step-by-step proof:
- The equation y = eˣ can be rewritten as ln y = x.
- Differentiate both sides of this equation and use the chain rule:
1/y × dy/dx = 1
dy/dx = y
- Since y = eˣ, therefore dy/dx = eˣ.