CAL007 · Calculus · Classes 11–12
Quotient rule
The derivative of a quotient is (u′v − uv′)/v².
(u/v)′Quotient rule
📐 Formula
(u/v)′ = (u′v − uv′) / v²
✏️ Worked example
y = x²/(x + 1): y′ = (2x(x + 1) − x²)/(x + 1)² = (x² + 2x)/(x + 1)²; at x = 1, y′ = 3/4.
🌍 Where it is used
Rates of ratios, such as average cost per item.
❓ Quick check
d/dx (1/x) = ?
🏋️ Practice
Easyd/dx (x/(x + 1))?
Answer: 1/(x + 1)²
Mediumd/dx (sin x / x) at x = π?
Answer: −1/π
Challenged/dx tan x (as sin/cos)?
Answer: sec² x