Standard derivatives (must memorize): (1) d/dx[xⁿ] = nxⁿ⁻¹; (2) d/dx[eˣ] = eˣ; (3) d/dx[aˣ] = aˣ ln a; (4) d/dx[ln x] = 1/x; (5) d/dx[sin x] = cos x; (6) d/dx[cos x] = -sin x; (7) d/dx[tan x] = sec² x; (8) d/dx[cot x] = -csc² x. Constants: d/dx[c] = 0. Linear: d/dx[cx] = c. Example: f(x) = eˣ sin x. Using product rule: f'(x) = eˣ sin x + eˣ cos x = eˣ(sin x + cos x). Shortcuts: Create derivative table for quick reference. Exam tip: Memorize top 8 derivatives. Use rules to combine them efficiently. Practice: Apply to polynomials, exponentials, trigonometric functions.