(f(g(x)))' = f'(g(x))⋅g'(x) V = (4/3)πr³ c = λf α + β = -b/a E = E° - (0.0591/n) log Q v² = u² + 2as d/dx(e^x) = e^x E = VIt cos 2θ = cos²θ - sin²θ V = L(dI/dt) m = f'(x) d/dx(ln x) = 1/x P_solution = X_solvent × P^°_solvent A = Pe^rt A = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| Φ = BA cosθ s = (a+b+c)/2, A = √(s(s-a)(s-b)(s-c)) P(n, r) = n!/(n-r)! e = (v₂ - v₁)/(u₁ - u₂) n₁ sinθ₁ = n₂ sinθ₂ f(x) = Σ_n=0∞ (f⁽ⁿ⁾(0)/n!)xⁿ P = IV E = hf 1/f = 1/v + 1/u sin 2θ = 2 sinθ cosθ

F = k( q₁q₂ )/r² S = a/(1 - r) T = 2π√(L/g) M = moles/volume f'(a) = lim_h→0 (f(a+h)-f(a))/h m = (y₂ - y₁)/(x₂ - x₁) s = ut + ½at² log_b a = ln a/ln b lim_x→a f(x)/g(x) = lim_x→a f'(x)/g'(x) d = |Ax₀ + By₀ + C|/√(A²+B²) (Σ a_i²)(Σ b_i²) ≥ (Σ a_ib_i)² sin A + sin B = 2 sin((A+B)/2) cos((A-B)/2) F_c = mv²/r αβ = c/a f(x) = Σ_n=0∞ (f⁽ⁿ⁾(a)/n!)(x-a)ⁿ V = IR sin x = Σ (-1)ⁿ x⁽²ⁿ⁺¹⁾/(2n+1)! (1+x)ⁿ = Σ ⁿ C _k.x^k Normality = Molarity × n π = MRT x = [-b ± √(b² - 4ac)]/(2a) I = ½ Σ c_i z_i² ΔT_b = iK_bm A = ½ab sin C ΔG = ΔH - TΔS

p = mv ΔT_f = iK_fm Percent Purity = (mass of pure substance/mass of sample) × 100 2 sin A cos B = sin(A+B) + sin(A-B) F_x + F_y(dy/dx) = 0 d/dx(cos x) = -sin x F = ma ∫ u dv = uv - ∫ v du a_c = v²/r (x-h)² + (y-k)² = r² sin²(θ/2) = (1 - cosθ)/2 Q = It v = u + at n = c/v K_c = ([C]^c[D]^d)/([A]^a[B]^b) Equivalent Weight = Molecular Weight/n x = a sinθ pH = -log[H⁺] n = mass/M Rate = k[A]^m[B]ⁿ λ = h/p A = ∫_a^b f(x) dx W = Fd cosθ d/dx(sin x) = cos x a_n = a + (n - 1)d

K.E. = ½mv² ε = -dΦ/dt e^x = Σ xⁿ/n! ln(P₂/P₁) = -ΔH_vap/R (1/T₂ - 1/T₁) pK_a = -log K_a P = W/t f''(x) S_n = a(1 - rⁿ)/(1 - r) C(n, r) = n!/(r!(n-r)!) a_n = ar^{n - 1} U = mgh A = ab sinθ sin²θ + cos²θ = 1 S_n = (n/2)[2a + (n - 1)d] F = q(E + v × B) (a+b)ⁿ = Σ_k=0ⁿ (nCk)a^n-kb^k A = πab ∫(dx/x) = ln|x| + C d = √((x₂-x₁)²+(y₂-y₁)²) y - y₁ = m(x - x₁) cos²(θ/2) = (1 + cosθ)/2 cos x = Σ (-1)ⁿ x⁽²ⁿ⁾/(2n)!