d/dx(e^x) = e^x S_n = a(1 - rⁿ)/(1 - r) d = √((x₂-x₁)²+(y₂-y₁)²) V = L(dI/dt) e = (v₂ - v₁)/(u₁ - u₂) P_solution = X_solvent × P^°_solvent n = c/v a_c = v²/r cos 2θ = cos²θ - sin²θ c = λf sin²θ + cos²θ = 1 ln(P₂/P₁) = -ΔH_vap/R (1/T₂ - 1/T₁) S = a/(1 - r) P = W/t I = ½ Σ c_i z_i² P = IV S_n = (n/2)[2a + (n - 1)d] E = hf cos x = Σ (-1)ⁿ x⁽²ⁿ⁾/(2n)! Q = It (1+x)ⁿ = Σ ⁿ C _k.x^k A = ab sinθ a_n = a + (n - 1)d ΔG = ΔH - TΔS αβ = c/a

m = f'(x) (x-h)² + (y-k)² = r² V = IR V = (4/3)πr³ T = 2π√(L/g) f(x) = Σ_n=0∞ (f⁽ⁿ⁾(a)/n!)(x-a)ⁿ f(x) = Σ_n=0∞ (f⁽ⁿ⁾(0)/n!)xⁿ x = a sinθ m = (y₂ - y₁)/(x₂ - x₁) A = ½ab sin C F_c = mv²/r cos²(θ/2) = (1 + cosθ)/2 π = MRT A = Pe^rt W = Fd cosθ E = E° - (0.0591/n) log Q K.E. = ½mv² lim_x→a f(x)/g(x) = lim_x→a f'(x)/g'(x) n = mass/M (f(g(x)))' = f'(g(x))⋅g'(x) Rate = k[A]^m[B]ⁿ v² = u² + 2as P(n, r) = n!/(n-r)! 1/f = 1/v + 1/u Φ = BA cosθ

U = mgh d/dx(cos x) = -sin x E = VIt d/dx(sin x) = cos x a_n = ar^{n - 1} ε = -dΦ/dt p = mv Percent Purity = (mass of pure substance/mass of sample) × 100 log_b a = ln a/ln b f''(x) ∫(dx/x) = ln|x| + C F_x + F_y(dy/dx) = 0 C(n, r) = n!/(r!(n-r)!) A = ∫_a^b f(x) dx y - y₁ = m(x - x₁) Equivalent Weight = Molecular Weight/n v = u + at A = πab F = ma ∫ u dv = uv - ∫ v du (Σ a_i²)(Σ b_i²) ≥ (Σ a_ib_i)² λ = h/p f'(a) = lim_h→0 (f(a+h)-f(a))/h F = q(E + v × B) α + β = -b/a

M = moles/volume pH = -log[H⁺] sin 2θ = 2 sinθ cosθ K_c = ([C]^c[D]^d)/([A]^a[B]^b) s = (a+b+c)/2, A = √(s(s-a)(s-b)(s-c)) n₁ sinθ₁ = n₂ sinθ₂ sin A + sin B = 2 sin((A+B)/2) cos((A-B)/2) x = [-b ± √(b² - 4ac)]/(2a) sin²(θ/2) = (1 - cosθ)/2 Normality = Molarity × n sin x = Σ (-1)ⁿ x⁽²ⁿ⁺¹⁾/(2n+1)! pK_a = -log K_a s = ut + ½at² A = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| 2 sin A cos B = sin(A+B) + sin(A-B) ΔT_b = iK_bm e^x = Σ xⁿ/n! (a+b)ⁿ = Σ_k=0ⁿ (nCk)a^n-kb^k d/dx(ln x) = 1/x ΔT_f = iK_fm F = k( q₁q₂ )/r² d = |Ax₀ + By₀ + C|/√(A²+B²)