Description
Derivative f'(a) = lim (f(x)-f(a))/(x-a). Chain rule, product rule. Rolle's theorem, Mean Value Theorem. Taylor expansion with remainder.
Dependency Flowchart
Note: Arrows mean "depends on". Assumes Charts 1–2.
graph TD
D1["Def: Derivative\nf' a = lim diff quot"]
D2["Def: Differentiable\nf' exists"]
T1["Thm: Chain rule\n(f∘g)' = f'∘g · g'"]
T2["Thm: Product rule\nfg' = f'g + fg'"]
T3["Thm: Rolle\nf cont diff, f a = f b ⇒ f' c = 0"]
T4["Thm: MVT\nf b - f a = f' c b - a"]
T5["Thm: Taylor\nf = P_n + R_n"]
D1 --> D2
D1 --> T1
D1 --> T2
D2 --> T3
T3 --> T4
D1 --> T5
classDef definition fill:#b197fc,color:#fff,stroke:#9775fa
classDef theorem fill:#51cf66,color:#fff,stroke:#40c057
class D1,D2 definition
class T1,T2,T3,T4,T5 theorem
Color Scheme
Blue
Definitions
Definitions
Teal
Theorems
Theorems
Process Statistics
- Nodes: 7
- Edges: 8
- Definitions: 2
- Theorems: 5