chain rule
Nested function differentiation
The chain rule is a formula in calculus for finding the derivative of a composite function—a function built from other functions.
If y depends on u and u depends on x, the chain rule states that dy/dx equals dy/du times du/dx.
Use the chain rule to differentiate sin(x²).
The rule extends to functions with multiple layers of composition.
Function's rate of change
- partial derivativeDifferentiation fixing other variables
- differentiableHaving a derivative
- continuityUninterrupted progression or coherence
- tangent lineCurve-touching straight path
slope · gradient · infinitesimal · increment · limit · u-substitution · backpropagation
Directed rate of motion
- accelerationRate velocity changes
- rate of changeMeasure of variation speed
- kinematicsStudy of movement itself
- dynamicsStudy of forces
motion · flow · flux · growth rate · decay rate · optimization · physics · engineering
derivative
Function's rate of change
- partial derivativeDifferentiation fixing other variables
- differentiableHaving a derivative
- continuityUninterrupted progression or coherence
tangent line · slope · gradient · infinitesimal · increment · limit · u-substitution · backpropagation
velocity
Directed rate of motion
- accelerationRate velocity changes
- rate of changeMeasure of variation speed
- kinematicsStudy of movement itself
dynamics · motion · flow · flux · growth rate · decay rate · optimization · physics · engineering · economics
- probabilityprobability, chance, random, randomness, odds
- Formulaschemical formula, quadratic formula, empirical formula, area formula, volume formula
- Math RulesPythagorean theorem, distributive property, commutative property, associative property, order of operations
- calculusderivatives, integral, integrals, limits, differential calculus
- neural networksneural network, neural networks, hidden layers, backpropagation, layers
- Autodiffbackpropagation, gradients, partial derivative, derivative