e Calculator | ex
Calculate e raised to any power with step-by-step solutions and mathematical insights
Calculate ex
Any real number (positive, negative, or decimal)
Precision for result display
e1
Where e ≈ 2.7182818285
Results
2.7182818285
Exact Value
2.718281828e+0
Scientific Notation
Taylor Series Approximation
2.7182818285
Derivative
2.7182818285
d/dx(ex) = ex
Inverse (ln)
1.0000000000
ln(ex) = x
Interpretation
e¹ = e ≈ 2.718... (Euler's number itself)
Step-by-Step Solution
1.Calculate e^1
2.Using Euler's number e ≈ 2.7182818285
3.e^1 = 2.7182818285
4.Taylor series: e^x = 1 + x + x²/2! + x³/3! + ...
5.Taylor approximation: 2.7182818285
6.Derivative: d/dx(e^x) = e^x = 2.7182818285
About Euler's Number (e)
Value
e ≈ 2.718281828459...
Definition
lim(n→∞) (1 + 1/n)ⁿ
Taylor Series
e = 1 + 1/1! + 1/2! + 1/3! + ...
Properties of ex
•
Derivative
d/dx(ex) = ex
•
Always Positive
ex > 0 for all real x
•
Exponential Growth
Increases rapidly for x > 0
•
Inverse Function
ln(ex) = x
Understanding the Exponential Function ex
What is Euler's Number?
Euler's number (e) is a mathematical constant approximately equal to 2.718281828. It's the base of natural logarithms and appears frequently in mathematics, particularly in calculus, complex analysis, and many applications involving growth and decay.
Applications
- •Compound interest calculations
- •Population growth models
- •Radioactive decay
- •Probability distributions
Mathematical Properties
Taylor Series
ex = 1 + x + x²/2! + x³/3! + x⁴/4! + ...
Exponential Rules
ea × eb = ea+b
ea ÷ eb = ea-b
(ea)b = eab
Special Values
e⁰ = 1
e¹ = e ≈ 2.718
e⁻¹ = 1/e ≈ 0.368
eln(x) = x