Derivatives, Gradients, Jacobians and Hessians – Oh My!

Explains the mathematical concepts of derivatives, gradients, Jacobians, and Hessians and their relationships. Covers how derivatives measure function changes, gradients extend this to multivariable functions pointing toward steepest increase, Jacobian matrices describe space warping for vector-valued functions, and Hessian matrices capture second derivatives for understanding function curvature. Demonstrates practical applications in optimization algorithms like gradient descent, computer graphics rendering, and machine learning.