Manual Differentiation
Manual differentiation is a mathematical technique for computing derivatives of functions by hand, using rules like the chain rule, product rule, and quotient rule, without relying on automated tools. It involves deriving explicit formulas for derivatives through symbolic manipulation, often applied in fields like calculus, optimization, and machine learning for gradient-based methods. This approach provides exact derivatives but can be error-prone and time-consuming for complex functions.
Developers should learn manual differentiation when implementing custom algorithms in machine learning, physics simulations, or numerical optimization that require precise control over gradient calculations, such as in backpropagation for neural networks or solving differential equations. It is essential for debugging automated differentiation tools, understanding the underlying mathematics of models, and in educational contexts to build foundational skills in calculus and computational methods.