Derivative calculation rules:

• First Derivative: f'(x) or d/dx[f(x)]
• Second Derivative: f''(x) or d²/dx²[f(x)]
• n-th Derivative: f⁽ⁿ⁾(x) or dⁿ/dxⁿ[f(x)]

Examples:

• \[\frac{d}{dx}[x^2] = 2x\]
• \[\frac{d}{dx}[\sin(x)] = \cos(x)\]
• \[\frac{d^2}{dx^2}[x^3] = 6x\]