Derivative Rules
d/dx(c) = 0
d/dx(xⁿ) = nxⁿ⁻¹
d/dx(eˣ) = eˣ
d/dx(ln x) = 1/x
d/dx(sin x) = cos x
d/dx(cos x) = -sin x
d/dx(tan x) = sec²x
Chain & Product Rules
Chain: d/dx[f(g(x))] = f'(g(x))g'(x)
Product: d/dx[fg] = f'g + fg'
Quotient: d/dx[f/g] = (f'g - fg') / g²
Common Integrals
∫xⁿ dx = xⁿ⁺¹/(n+1) + C
∫eˣ dx = eˣ + C
∫(1/x) dx = ln|x| + C
∫sin x dx = -cos x + C
∫cos x dx = sin x + C
Limits
lim(x→0) sin(x)/x = 1
lim(x→∞) (1 + 1/x)ˣ = e
LHopital: lim f/g = lim f'/g'