COMPLETE FULL COURSE EDITION
DIFFERENTIATION MASTERCLASS
NOTES
Comprehensive 12th Class Calculus Package (Basic Rules to Advanced
Derivatives)
PAGE 1: FUNDAMENTAL ALGEBRAIC RULES
S.No. Function Expression Derivative Result (dy/dx)
1. d/dx (xⁿ) n · xⁿ⁻¹ ; (n ∈ ℝ)
2. d/dx (x) 1
3. d/dx (1/x) -1 / x²
4. d/dx (√x) 1 / (2√x)
5. d/dx (1 / √x) -1 / (2x³ᐟ²)
6. d/dx (k) 0 ; (k = non-zero constant)
7. d/dx [k · F(x)] k · d/dx(f(x)) = k · f'(x)
⚡ Complete Master Class Notes: Differentiation Series ⚡ Page 1
, PAGE 2: ALGEBRA OF DERIVATIVES
Let u and v be differentiable functions of x:
1. Addition Rule:
d/dx (u + v) = du/dx + dv/dx
2. Subtraction Rule:
d/dx (u - v) = du/dx - dv/dx
3. Product Rule (Leibniz Rule):
d/dx (u · v) = u · (dv/dx) + v · (du/dx)
4. Quotient Rule:
d/dx (u / v) = [ v · (du/dx) - u · (dv/dx) ] / v²
⚡ Complete Master Class Notes: Differentiation Series ⚡ Page 2
DIFFERENTIATION MASTERCLASS
NOTES
Comprehensive 12th Class Calculus Package (Basic Rules to Advanced
Derivatives)
PAGE 1: FUNDAMENTAL ALGEBRAIC RULES
S.No. Function Expression Derivative Result (dy/dx)
1. d/dx (xⁿ) n · xⁿ⁻¹ ; (n ∈ ℝ)
2. d/dx (x) 1
3. d/dx (1/x) -1 / x²
4. d/dx (√x) 1 / (2√x)
5. d/dx (1 / √x) -1 / (2x³ᐟ²)
6. d/dx (k) 0 ; (k = non-zero constant)
7. d/dx [k · F(x)] k · d/dx(f(x)) = k · f'(x)
⚡ Complete Master Class Notes: Differentiation Series ⚡ Page 1
, PAGE 2: ALGEBRA OF DERIVATIVES
Let u and v be differentiable functions of x:
1. Addition Rule:
d/dx (u + v) = du/dx + dv/dx
2. Subtraction Rule:
d/dx (u - v) = du/dx - dv/dx
3. Product Rule (Leibniz Rule):
d/dx (u · v) = u · (dv/dx) + v · (du/dx)
4. Quotient Rule:
d/dx (u / v) = [ v · (du/dx) - u · (dv/dx) ] / v²
⚡ Complete Master Class Notes: Differentiation Series ⚡ Page 2
