Answer:
ds = √(dx² + dy²)
ds = √(1 + (dy/dx)²) dx
ds = √(1 + (dx/dy)²) dy
Step-by-step explanation:
Arc length ds is found with Pythagorean theorem:
ds² = dx² + dy²
Solving for ds:
ds = √(dx² + dy²)
If we factor out dx from the radical:
ds = √(dx² (1 + (dy/dx)²))
ds = √(1 + (dy/dx)²) dx
Or, if we factor out dy from the radical:
ds = √(dy² ((dx/dy)² + 1))
ds = √(1 + (dx/dy)²) dy
