Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. It’s essential for understanding change and motion.

Differential Calculus

Derivatives

The derivative of a function represents the rate of change at any given point.

Basic derivative rules:

• Power rule: d/dx(x^n) = nx^(n-1)
• Product rule: d/dx(fg) = f’g + fg’
• Chain rule: d/dx(f(g(x))) = f’(g(x))g’(x)

Applications

• Finding slopes of tangent lines
• Optimization problems
• Related rates

Integral Calculus

Integrals

Integration is the reverse process of differentiation, used to find areas under curves.

Basic integration rules:

• ∫x^n dx = x^(n+1)/(n+1) + C
• ∫e^x dx = e^x + C
• ∫sin(x) dx = -cos(x) + C

Applications

• Finding areas and volumes
• Solving differential equations
• Physics applications (work, energy)

Getting Started

Practice with simple functions first, then gradually work up to more complex problems. Remember that calculus is the foundation for many advanced mathematical concepts!