Enter any number to compute e to the power of x (eˣ)
ex =
Calculation Result
e =
Detailed Derivation
Exponential Formula
ex = exp(x) ≈ 2.71828x
e is the base of natural logarithms, approximately 2.71828... eˣ is one of the most important functions in mathematics, appearing widely in calculus, probability and compound interest.
⚠Note: e ≈ 2.71828. For large x, eˣ grows extremely fast and results may be displayed in scientific notation.
What is the Exponential Function?
The exponential function eˣ is one of the most important functions in mathematics, with the unique property that its derivative equals itself.
Natural Constant e
e ≈ 2.71828..., an irrational number defined by the limit lim(1+1/n)ⁿ as n → ∞.
Unique Derivative
(d/dx)eˣ = eˣ — the only function with this property, making it fundamental in calculus.
Growth Behavior
For x > 0, eˣ grows extremely fast; for x < 0, eˣ approaches 0 but never reaches it.
Compound Interest
e is intimately linked to compound interest: 100% annual interest compounded continuously approaches e.
💡 Example: e¹ = e ≈ 2.71828; e² ≈ 7.38906; e⁻¹ = 1/e ≈ 0.36788. eˣ is always positive regardless of whether x is positive or negative.
e ≈ 2.71828..., the base of natural logarithms. It is an irrational number defined by the limit lim(1+1/n)ⁿ as n approaches infinity.
What is e^x vs exp(x)?▼
exp(x) is simply another notation for eˣ. They are completely equivalent. In math and programming, exp(x) commonly denotes e to the power of x.
How do you compute e to a negative power?▼
e to a negative power equals its reciprocal. e⁻¹ = 1/e ≈ 0.3679, e⁻² = 1/e² ≈ 0.1353. Results are always positive and approach 0 as the exponent decreases.
What is the derivative of e^x?▼
The derivative of eˣ is itself: (d/dx)eˣ = eˣ. This unique property makes eˣ extremely important in calculus and differential equations.
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