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Derivative

Calculus Derivative

The instantaneous rate of change of a function with respect to its variable, representing the slope of the tangent line.

技术细节

Derivative functions relate angles to side ratios in right triangles. In computing, angles are typically in radians (π radians = 180°). Key identities: sin²θ + cos²θ = 1, sin(2θ) = 2sinθcosθ. Applications include wave generation (audio synthesis), rotation transforms (2D/3D graphics), signal processing (Fourier analysis), and geolocation (haversine formula for great-circle distance). JavaScript's Math.sin() expects radians, so convert degrees with: radians = degrees × π / 180.

示例

```
Derivative calculation:

  Input:  value = 42
  Apply derivative: result = f(42)
  Output: result
```

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