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1 Introduction 2 Review: Scalar derivative rules 3 Introduction to vector calculus and partial derivatives 4 Matrix calculus 4.1 Generalization of the Jacobian 4.2 Derivatives of vector element-wise binary operators 4.3 Derivatives involving scalar expansion 4.4 Vector sum reduction 4.5 The Chain Rules 4.5.1 Single-variable chain rule 4.5.2 Single-variable total-derivative chain rule 4.5.3 Vector chain rule 5 The gradient of neuron activation 6 The gradient of the neural network loss function 6.1 The gradient with respect to the weights 6.2 The derivative with respect to the bias 7 Summary 8 Matrix Calculus Reference 8.1 Gradients and Jacobians 8.2 Element-wise operations on vectors 8.3 Scalar expansion 8.4 Vector reductions 8.5 Chain rules 9 Notation 10 Resources