Skip to content
Mathify
Esta calculadora se muestra actualmente en inglés mientras se prepara su traducción.

Matematicas

Calculadora verificada con fórmula transparente

Matematicas

Hyperbolic Tangent Calculator.

Computes the hyperbolic tangent of a given real number, useful in math, physics, and machine learning.

Los resultados se actualizan en vivo mientras escribes.
ƒ

Tus entradas

Cómo funciona

  1. 1

    Enter the value of x.

  2. 2

    Compute e^(2x) using the exponential function.

  3. 3

    Subtract 1 from e^(2x) to get the numerator.

  4. 4

    Add 1 to e^(2x) to get the denominator, then divide numerator by denominator.

(exp(2*x)-1)/(exp(2*x)+1)

Preguntas frecuentes

What is the range of tanh(x)?

The hyperbolic tangent always outputs values between -1 and 1, approaching -1 as x goes to negative infinity and 1 as x goes to positive infinity.

How is tanh(x) related to sinh and cosh?

tanh(x) = sinh(x) / cosh(x), where sinh(x) = (e^x - e^(-x))/2 and cosh(x) = (e^x + e^(-x))/2.

Why use tanh in neural networks?

Because its output is zero-centered and bounded, which helps with gradient stability during training.

Explorar esta categoría de calculadoras

MatematicasExplorar todo

Resultados

Fórmula verificada

tanh(x)

0,762

Pregunta lo que sea

Estimación solo como guía general: verifica decisiones importantes con un profesional adecuado.

Cómo funciona

Computes the hyperbolic tangent of a given real number, useful in math, physics, and machine learning.

  1. Enter the value of x.
  2. Compute e^(2x) using the exponential function.
  3. Subtract 1 from e^(2x) to get the numerator.
  4. Add 1 to e^(2x) to get the denominator, then divide numerator by denominator.

Fórmulas

Las matemáticas detrás de esta calculadora, escritas para que puedas verificar el resultado.

Definition

tanh(x) = (e^(2x) - 1) / (e^(2x) + 1)

This is the standard formula for the hyperbolic tangent, expressed using the exponential function.

Example:

Input: x = 1

Calculation: (e^2 - 1) / (e^2 + 1)

Result: ≈ 0.761594

Casos de uso reales

Dónde aparece este cálculo en la vida cotidiana.

Activation function

Used in neural networks to introduce non-linearity while keeping outputs bounded.

Example: Squashing neuron outputs to [-1, 1].

Hyperbolic geometry

Appears in formulas for the Gudermannian function and in special relativity.

Example: Rapidity in physics: φ = atanh(v/c).

Consejos y errores comunes

Tips

  • For large |x|, tanh(x) approaches ±1; use the formula directly to avoid overflow.
  • If your calculator lacks tanh, use the exponential form.
  • Remember tanh is odd: tanh(-x) = -tanh(x).

Common Mistakes to Avoid

  • Confusing tanh with arctan (inverse tangent).
  • Using degrees instead of radians when x is an angle.
  • Forgetting that tanh(0) = 0, not 1.

Supuestos y limitaciones

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.