Last updated: Jul 29, 2024

e Calculator | eˣ | e Raised to Power of x

Q: 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.

Q: 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/e N , as N gets larger, e -N will get smaller, ending up at zero if N = ∞ .

Q: What is the derivative of e to the x?

The derivative of e ˣ is itself, e ˣ . Here is a step-by-step proof: The equation y = e ˣ can be rewritten as ln y = x . Differentiate both sides of this equation and use the chain rule: 1/ y × d y /d x = 1 d y /d x = y Since y = e ˣ , therefore d y /d x = e ˣ .

Table of contents

What is e on a calculator? – e to the x How to put e in a calculator? Calculate e to the x e calculator – examples FAQs

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:

\scriptsize \qquad \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \ldots

e is also a part of the most beautiful equation in mathematics: $e^{iπ} + 1 = 0$ 🌺

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 x?" 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 🤗

FAQs

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/e^N, 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.

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