Skip to content
Free public beta until December 4, 2026: every course is open, no card needed. After that, the first chapter of each course stays free and full access is a one-time $39 ($19 for up to 100 founding members chosen for helpful feedback). Your progress is kept. How the beta works

differentiation

The chain rule

taught

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Backpropagation in matrix form Backpropagation through time Choosing u -- recognizing a substitution,… Derivatives of inverse functions Gradient clipping Related rates in geometric scenes Related rates with volume and rate scenes Substitution with trigonometric and exponential integrands Tangent lines to implicit curves U-substitution with definite integrals -- changing limits vs.… Vanishing and exploding gradients What gradient descent and backpropagation do (primer) Backpropagation Chain rule with exponential and logarithmic functions Chain rule with trigonometric functions Combining the chain rule with the product and quotient rules FTC Part 1 with variable limits of integration -- the… Identifying composite-function structure for… Implicit differentiation The generalized power rule The related-rates method U-substitution -- reversing the chain rule for indefinite… The chain rule Basic antiderivative rules -- power, constant multiple,… Computational graphs Constant, power, and constant-multiple rules Derivatives of trigonometric functions Differentiability and continuity Evaluate logarithms L'Hopital's Rule: 0/0 and infinity/infinity Linear approximation Newton's method Rates of change in the sciences The Fundamental Theorem of Calculus, Part 1 -- the… The derivative as a function The product rule The quotient rule Decompose composite functions The definition of the derivative Average vs. instantaneous rate of change Combine compose functions What a limit means

Click to expand

Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.