Calculus Guides

Use trig substitution to integrate expressions with square roots. Learn when to use sine, tangent, or secant substitutions with worked examples.

The Fundamental Theorem of Calculus links derivatives and integrals. Learn both parts with examples showing how to evaluate definite integrals.

Learn implicit differentiation for equations where y isn't solved explicitly. Step-by-step examples with circles, ellipses, and complex equations.

Solve related rates problems systematically. Learn the method with ladder, balloon, cone, and shadow examples worked out in detail.

Learn the essential derivative rules with clear examples. Power rule, product rule, quotient rule, and derivatives of common functions explained.

Master limit evaluation with direct substitution, factoring, rationalization, and squeeze theorem. Step-by-step examples for every technique.

L'Hôpital's rule handles 0/0 and infinity/infinity limits. Learn when to apply it, see step-by-step examples, and avoid common mistakes.

U-substitution reverses the chain rule for integration. Learn how to choose u, handle the differential, and solve integrals step by step.

The chain rule lets you find derivatives of nested functions. Learn the formula, see worked examples, and practice with common function types.

Learn the integration by parts formula and when to use it. Step-by-step examples with polynomial, exponential, and trigonometric functions.