/* ═══════════════════════════════════════════
CSS Variables — Calculus Master Theme
═══════════════════════════════════════════ */
:root {
–mcs-bg: #080C14;
–mcs-surface: #111829;
–mcs-surface2: #162033;
–mcs-border: #1E2D42;
–mcs-border2: #2D3E5D;
–mcs-blue: #3B82F6;
–mcs-blue-bright: #60A5FA;
–mcs-cyan: #22D3EE;
–mcs-blue-glow: rgba(59,130,246,0.12);
–mcs-text: #F1F5F9;
–mcs-text-muted: #94A3B8;
–mcs-text-dim: #475569;
–mcs-font-display: ‘Syne’, sans-serif;
–mcs-font-body: ‘DM Sans’, sans-serif;
–mcs-font-mono: ‘JetBrains Mono’, monospace;
}
.mcs-root-container {
all: initial;
display: block;
font-family: var(–mcs-font-body);
background: var(–mcs-bg);
color: var(–mcs-text);
min-height: 100vh;
}
*, *::before, *::after { box-sizing: border-box; margin: 0; padding: 0; }
/* Grid background */
.mcs-grid-bg {
position: fixed !important; inset: 0 !important; z-index: 0 !important; pointer-events: none !important;
background-image:
linear-gradient(rgba(59,130,246,0.02) 1px, transparent 1px),
linear-gradient(90deg, rgba(59,130,246,0.02) 1px, transparent 1px) !important;
background-size: 48px 48px !important;
}
.mcs-glow {
position: fixed !important; width: 800px !important; height: 400px !important;
background: radial-gradient(ellipse, rgba(34,211,238,0.06) 0%, transparent 70%) !important;
top: -100px !important; left: 50% !important; transform: translateX(-50%) !important;
pointer-events: none !important; z-index: 0 !important;
}
/* HERO */
.mcs-hero {
position: relative !important; z-index: 1 !important;
padding: 80px 24px 40px !important;
text-align: center !important; max-width: 1000px !important; margin: 0 auto !important;
}
.mcs-hero-label {
display: inline-flex !important; align-items: center !important; gap: 8px !important;
background: var(–mcs-blue-glow) !important;
border: 1px solid rgba(59,130,246,0.3) !important;
border-radius: 100px !important; padding: 5px 16px !important;
font-size: 12px !important; font-weight: 600 !important; color: var(–mcs-blue-bright) !important;
letter-spacing: 1.5px !important; text-transform: uppercase !important;
margin-bottom: 22px !important;
}
.mcs-h1 {
font-family: var(–mcs-font-display) !important;
font-size: clamp(32px, 6vw, 66px) !important;
font-weight: 800 !important; letter-spacing: -2px !important; line-height: 1.05 !important;
margin-bottom: 16px !important; color: var(–mcs-text) !important;
}
.mcs-h1 mark {
background: linear-gradient(135deg, var(–mcs-blue-bright), var(–mcs-cyan)) !important;
-webkit-background-clip: text !important; -webkit-text-fill-color: transparent !important;
background-clip: text !important;
}
.mcs-hero-sub {
font-size: clamp(15px, 2.2vw, 18px) !important; font-weight: 300 !important; color: var(–mcs-text-muted) !important;
line-height: 1.65 !important; max-width: 650px !important; margin: 0 auto 28px !important;
}
/* Interactivity */
.mcs-search-wrap { max-width: 520px !important; margin: 0 auto 40px !important; position: relative !important; }
.mcs-search {
width: 100% !important; background: var(–mcs-surface) !important;
border: 1px solid var(–mcs-border) !important; border-radius: 12px !important;
padding: 14px 16px 14px 44px !important; font-size: 16px !important; color: var(–mcs-text) !important; outline: none !important;
transition: border-color 0.2s, box-shadow 0.2s !important;
}
.mcs-search:focus { border-color: var(–mcs-blue-bright) !important; box-shadow: 0 0 0 3px rgba(59,130,246,0.1) !important; }
.mcs-tabs { display: flex !important; gap: 8px !important; justify-content: center !important; flex-wrap: wrap !important; max-width: 1000px !important; margin: 0 auto 48px !important; position: relative !important; z-index: 1 !important; }
.mcs-tab { background: var(–mcs-surface) !important; border: 1px solid var(–mcs-border) !important; border-radius: 100px !important; padding: 8px 18px !important; font-size: 14px !important; color: var(–mcs-text-muted) !important; cursor: pointer !important; transition: all 0.2s !important; }
.mcs-tab.mcs-active { background: var(–mcs-blue-glow) !important; border-color: var(–mcs-blue) !important; color: var(–mcs-blue-bright) !important; font-weight: 600 !important; }
/* LAYOUT */
.mcs-main { position: relative !important; z-index: 1 !important; max-width: 1200px !important; margin: 0 auto !important; padding: 0 24px !important; display: grid !important; grid-template-columns: 240px 1fr !important; gap: 40px !important; align-items: start !important; }
@media(max-width:960px){ .mcs-main{ grid-template-columns:1fr !important; } .mcs-sidebar{display:none !important;} }
.mcs-sidebar { position: sticky !important; top: 40px !important; }
.mcs-toc { list-style: none !important; display: flex !important; flex-direction: column !important; gap: 6px !important; }
.mcs-toc a { display: block !important; padding: 10px 14px !important; border-radius: 10px !important; font-size: 14px !important; color: var(–mcs-text-muted) !important; text-decoration: none !important; transition: all 0.2s !important; }
.mcs-toc a:hover { background: rgba(255,255,255,0.03) !important; color: var(–mcs-text) !important; }
.mcs-toc a.mcs-toc-active { color: var(–mcs-blue-bright) !important; background: var(–mcs-blue-glow) !important; font-weight: 600 !important; }
/* Cards Grid */
.mcs-formulas-grid { display: grid !important; grid-template-columns: repeat(auto-fill, minmax(340px, 1fr)) !important; gap: 18px !important; margin-bottom: 60px !important; }
.mcs-formula-card { background: var(–mcs-surface) !important; border: 1px solid var(–mcs-border) !important; border-radius: 16px !important; padding: 22px !important; transition: all 0.25s !important; position: relative !important; }
.mcs-formula-card:hover { border-color: var(–mcs-blue) !important; transform: translateY(-4px) !important; box-shadow: 0 10px 30px rgba(0,0,0,0.3) !important; }
.mcs-formula-card.mcs-hidden { display: none !important; }
.mcs-card-name { font-size: 14px !important; font-weight: 600 !important; color: var(–mcs-text-muted) !important; margin-bottom: 12px !important; display: flex !important; align-items: center !important; gap: 8px !important; }
.mcs-tag { font-size: 10px !important; padding: 2px 8px !important; border-radius: 4px !important; text-transform: uppercase !important; letter-spacing: 0.5px !important; font-weight: 700 !important; }
.mcs-tag-core { background: rgba(16,185,129,0.1) !important; color: #10B981 !important; }
.mcs-tag-adv { background: rgba(139,92,246,0.1) !important; color: #A78BFA !important; }
.mcs-formula-box { background: var(–mcs-bg) !important; border: 1px solid var(–mcs-border) !important; border-radius: 10px !important; padding: 16px !important; font-family: var(–mcs-font-mono) !important; font-size: 16px !important; color: var(–mcs-cyan) !important; line-height: 1.5 !important; position: relative !important; }
.mcs-card-desc { font-size: 13px !important; color: var(–mcs-text-dim) !important; margin-top: 12px !important; line-height: 1.6 !important; }
.mcs-section-header { display: flex !important; align-items: center !important; gap: 15px !important; margin: 60px 0 24px !important; padding-bottom: 15px !important; border-bottom: 1px solid var(–mcs-border) !important; }
.mcs-section-title { font-family: var(–mcs-font-display) !important; font-size: 26px !important; font-weight: 800 !important; color: var(–mcs-text) !important; }
.mcs-inline-cta { background: linear-gradient(135deg, var(–mcs-blue-glow), transparent) !important; border: 1px solid rgba(59,130,246,0.2) !important; border-radius: 20px !important; padding: 32px !important; display: flex !important; align-items: center !important; justify-content: space-between !important; gap: 24px !important; margin: 60px 0 !important; flex-wrap: wrap !important; }
.mcs-inline-btn { background: var(–mcs-blue) !important; color: #fff !important; padding: 14px 28px !important; border-radius: 12px !important; font-weight: 700 !important; text-decoration: none !important; font-size: 16px !important; transition: all 0.2s !important; }
.mcs-inline-btn:hover { background: var(–mcs-blue-bright) !important; transform: scale(1.02) !important; }
/* SEO / Content Sections */
.mcs-seo { max-width: 900px !important; margin: 80px auto !important; padding: 60px 24px !important; border-top: 1px solid var(–mcs-border) !important; }
.mcs-seo h2 { font-family: var(–mcs-font-display) !important; font-size: 32px !important; font-weight: 800 !important; margin: 40px 0 20px !important; color: var(–mcs-text) !important; }
.mcs-seo h3 { font-family: var(–mcs-font-display) !important; font-size: 22px !important; font-weight: 700 !important; margin: 30px 0 15px !important; color: var(–mcs-blue-bright) !important; }
.mcs-seo p { font-size: 17px !important; color: var(–mcs-text-muted) !important; line-height: 1.8 !important; margin-bottom: 24px !important; }
.mcs-seo ul { margin: 0 0 24px 24px !important; }
.mcs-seo li { font-size: 17px !important; color: var(–mcs-text-muted) !important; line-height: 1.7 !important; margin-bottom: 12px !important; }
/* Image Container */
.mcs-img-container { width: 100% !important; background: var(–mcs-surface) !important; border: 1px solid var(–mcs-border) !important; border-radius: 24px !important; margin: 40px 0 !important; overflow: hidden !important; box-shadow: 0 20px 50px rgba(0,0,0,0.4) !important; }
.mcs-img-container img { width: 100% !important; height: auto !important; display: block !important; }
📐 Advanced Calculus · Comprehensive 2026 Reference
Calculus Formula Sheet:From Limits to Series
The definitive guide for AP Calculus AB/BC and Engineering Math. Search over 100+ identities, derivatives, and integration rules. Accurate, printable, and completely free.
All Topics
Limits
Differentiation
Integration
Calculus Trig
Series & Taylor
Complex derivative giving you trouble?
Don’t just copy the answer. See the full derivation with our AI Camera Solver.
📷 Solve with Camera
No formulas found. Try searching for “log”, “chain”, or “integral”.
The Ultimate Calculus Cheat Sheet for Students
Calculus is the study of continuous change. Whether you are preparing for the AP Calculus exam or studying engineering at university, having a reliable source for
Differentiation and Integration formulas is key to your success. Our comprehensive reference sheet is updated for 2026 to include everything from foundational limits to advanced Taylor series expansions.
How to Use This Reference Successfully
Don’t just memorize — understand the relationships. For example, every integration rule on this page is effectively the “inverse” of a differentiation rule. When you see the derivative of
ln(x) is
1/x , you immediately know that the integral of
1/x must involve
ln(x) .
Limits: Master L’Hôpital’s Rule early. It is the most powerful tool for solving indeterminate forms on exams.
Derivatives: Focus on the Chain Rule. Over 70% of differentiation errors in exams come from forgetting to multiply by the inner function’s derivative.
Integrals: Memorize the common trigonometric integrals. While substitution (U-Sub) is common, recognizing the form of arctan or arcsin can save you minutes during a timed test.
Why Our Calculus Solver is Different
While this cheat sheet provides the formulas, our
Math Camera Solver provides the context. Most apps like Photomath show you a final answer but lock the steps behind a $9.99/mo paywall. We believe education should be free. If you find a problem on your homework that doesn’t match one of these formulas, take a photo and let our AI explain the derivation to you — for free.
(function(){
const searchInput = document.getElementById(‘mcs-search’);
const tabs = document.querySelectorAll(‘.mcs-tab’);
const cards = document.querySelectorAll(‘.mcs-formula-card’);
const sections = document.querySelectorAll(‘.mcs-section’);
const noResults = document.getElementById(‘mcs-no-results’);
function filterFormulas() {
const query = searchInput.value.toLowerCase().trim();
const activeTab = document.querySelector(‘.mcs-tab.mcs-active’).dataset.filter;
let visibleCount = 0;
cards.forEach(card => {
const tags = (card.dataset.tags || ”).toLowerCase();
const name = (card.dataset.name || ”).toLowerCase();
const content = card.querySelector(‘.mcs-formula-box’).textContent.toLowerCase();
const section = card.closest(‘section’).dataset.section;
const matchesSearch = name.includes(query) || tags.includes(query) || content.includes(query);
const matchesTab = activeTab === ‘all’ || section === activeTab;
if(matchesSearch && matchesTab) {
card.classList.remove(‘mcs-hidden’);
visibleCount++;
} else {
card.classList.add(‘mcs-hidden’);
}
});
sections.forEach(sec => {
const visibleInSec = sec.querySelectorAll(‘.mcs-formula-card:not(.mcs-hidden)’).length;
sec.style.display = visibleInSec > 0 ? ‘block’ : ‘none’;
});
noResults.style.display = (visibleCount === 0) ? ‘block’ : ‘none’;
}
searchInput.addEventListener(‘input’, filterFormulas);
tabs.forEach(tab => {
tab.addEventListener(‘click’, () => {
tabs.forEach(t => t.classList.remove(‘mcs-active’));
tab.classList.add(‘mcs-active’);
filterFormulas();
});
});
// TOC Tracking
const tocLinks = document.querySelectorAll(‘.mcs-toc-link’);
window.addEventListener(‘scroll’, () => {
let fromTop = window.scrollY + 100;
sections.forEach(sec => {
if (sec.offsetTop fromTop) {
tocLinks.forEach(link => {
link.classList.toggle(‘mcs-toc-active’, link.getAttribute(‘href’).substring(1) === sec.id);
});
}
});
});
})();