LIMITS_&_CHAIN
The Derivative (df/dx)
The instantaneous rate of change. Essential for backpropagation and optimization in machine learning algorithms.
f'(x) = lim h→0 [f(x+h) - f(x)] / hIntegration (∫)
The accumulation of values. Finding areas under curves and total probability distributions.
Area = ∫ f(x) dxOPTIMIZATION
GRADIENT
DESCENT
DESCENT
θ = θ - α ∇J(θ)
Finding the GLOBAL MINIMUM of the cost function.
CALC_MODULES
Power Rule
d/dx (x^n) = nx^(n-1)
Chain Rule
Derivatives of composite functions.
Taylor Series
Function approximation via polynomials.
Partial Derivs
Calculus in multi-variable spaces.