Derivatives Of Composite Functions Chain Rule Tt Theorem And Its Proof

graph TD; A[Derivatives of composite functions: Chain Rule] --> B((Theorem)) A --> C((Proof)) B --> D{f(g(x))} B --> E{g'(x)} C --> F{Step 1} C --> G{Step 2} D --> H((f'(g(x)))) E --> I((f(g(x)))) F --> J((Assume h(x) = g(f(x)))) G --> K(Differentiate h(x) with respect to x) H --> L((Multiply f'(g(x)) by g'(x))) I --> M((Result is the derivative of the composite function)) J → N((This is the composite function)) K --> O((This gives h'(x))) L --> P((This is the Chain Rule)) M --> P N --> O