Class 12 Maths: Formula Sheet
1. Differentiation
• d/dx (sin x) = cos x
• d/dx (cos x) = -sin x
• d/dx (tan x) = sec²x
• d/dx (log x) = 1/x
• d/dx (eˣ) = eˣ
• d/dx (aˣ) = aˣ log a
Chain Rule: dy/dx = (dy/du) * (du/dx)
2. Integration (Indefinite)
• ∫ xⁿ dx = (xⁿ⁺¹)/(n+1) + C
• ∫ (1/x) dx = log|x| + C
• ∫ eˣ dx = eˣ + C
• ∫ sin x dx = -cos x + C
• ∫ tan x dx = log|sec x| + C
ILATE Rule for Integration by Parts:
∫ u.v dx = u ∫ v dx - ∫ [u' ∫ v dx] dx
3. Inverse Trig Functions
• sin⁻¹x + cos⁻¹x = π/2
• tan⁻¹x + cot⁻¹x = π/2
• tan⁻¹x + tan⁻¹y = tan⁻¹[(x+y)/(1-xy)]
1. Differentiation
• d/dx (sin x) = cos x
• d/dx (cos x) = -sin x
• d/dx (tan x) = sec²x
• d/dx (log x) = 1/x
• d/dx (eˣ) = eˣ
• d/dx (aˣ) = aˣ log a
Chain Rule: dy/dx = (dy/du) * (du/dx)
2. Integration (Indefinite)
• ∫ xⁿ dx = (xⁿ⁺¹)/(n+1) + C
• ∫ (1/x) dx = log|x| + C
• ∫ eˣ dx = eˣ + C
• ∫ sin x dx = -cos x + C
• ∫ tan x dx = log|sec x| + C
ILATE Rule for Integration by Parts:
∫ u.v dx = u ∫ v dx - ∫ [u' ∫ v dx] dx
3. Inverse Trig Functions
• sin⁻¹x + cos⁻¹x = π/2
• tan⁻¹x + cot⁻¹x = π/2
• tan⁻¹x + tan⁻¹y = tan⁻¹[(x+y)/(1-xy)]
