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Term 6 · Year 2

Term 6 — Derivatives: Concept and Rules

Definition via limit, rules (chain, product, quotient), notable derivatives.

10 lessons  ·  10 published ·  ~32h of study

(Year 2 — Differential Calculus and Probability)

Classes (didactic grouping)

Each Class groups 2–5 Lessons by topic. Click on a Lesson to study the content.

Class A — Definition of the derivative and basic rules

~6h · 2 lessons
  1. Lesson 51
    Derivative: definition via limit
    f'(a) = lim (f(a+h)-f(a))/h, tangent line
    published →
  2. Lesson 52
    Differentiation Rules
    (f+g)', (fg)', (f/g)', power rule
    published →

Class B — Chain rule and implicit differentiation

~6h · 2 lessons
  1. Lesson 53
    The Chain Rule
    (f∘g)' = f'(g)·g'
    published →
  2. Lesson 54
    Implicit Differentiation
    F(x,y)=0, dy/dx
    published →

Class C — Higher order, inverse and linear approximation

~9h · 3 lessons
  1. Lesson 55
    Higher-Order Derivatives
    f''(x), f^(n)
    published →
  2. Lesson 56
    Derivatives of Inverse Functions
    (f⁻¹)'(y) = 1/f'(x)
    published →
  3. Lesson 57
    Linear Approximation and Differentials
    L(x) = f(a) + f'(a)(x-a), differentials
    published →

Class D — Related rates + smoothness

~9h · 3 lessons
  1. Lesson 58
    Related Rates
    Sliding ladder, volume of expanding sphere, etc.
    published →
  2. Lesson 59
    Differentiability and Smoothness
    Continuity, corners, vertical tangents, cusps
    published →
  3. Lesson 60
    Term 6 Consolidation: Derivatives
    Synthesis: 60 mixed derivative problems
    published →

Test yourself this term

There are 10 exam versions covering this term, each with answer key + step-by-step solutions. Take one after each group of lessons.

Open exams for Term 6 →