Calculus for Beginners: Derivatives & Integration Rules Cheat Sheet

Calculus is the study of continuous change. It is split into two major branches: Differential Calculus (rates of change / slopes) and Integral Calculus (accumulation / areas under curves).

• Power Rule: d/dx [xⁿ] = n · xⁿ⁻¹
• Constant Rule: d/dx [c] = 0
• Product Rule: d/dx [f · g] = f'g + fg'
• Quotient Rule: d/dx [f / g] = (f'g − fg') / g²
• Chain Rule: d/dx [f(g(x))] = f'(g(x)) · g'(x)

• Power Rule for Integrals: ∫ xⁿ dx = (xⁿ⁺¹ / (n + 1)) + C (for n ≠ -1)
• Natural Log Integral: ∫ (1/x) dx = ln|x| + C
• Exponential Integral: ∫ eˣ dx = eˣ + C