In ML, functions don't have just one input ($x$); they have thousands or millions of inputs (weights and biases). Partial derivatives allow us to calculate the slope relative to a single variable while keeping others constant.
If you are diving into Machine Learning (ML) or Data Science, you have likely realized one thing very quickly: calculus for machine learning pdf link
wnew=wold−η⋅∇J(w)w sub n e w end-sub equals w sub o l d end-sub minus eta center dot nabla cap J open paren w close paren (eta) is the learning rate. 3. The Chain Rule: The Logic of Backpropagation In ML, functions don't have just one input
textbook, which offers a full PDF covering the foundations of multivariate calculus specifically for ML applications. Mathematics for Machine Learning Core Pillars of Calculus in Machine Learning Calculus in ML primarily focuses on Differential Calculus Chain Rule specifically to a simple neural network layer
: A dense reference for identities involving derivatives of vectors and matrices. Chain Rule specifically to a simple neural network layer?