Chain rule (disambiguation)

Chain rule may refer to:

• Chain rule in calculus:

$\frac {\mathrm dy}{\mathrm dx} = \frac {\mathrm dy} {\mathrm du} \cdot\frac {\mathrm du}{\mathrm dx}.$

• Cyclic chain rule, or triple product rule:

$\left({\frac {\partial x}{\partial y}}\right)_{z}\left({\frac {\partial y}{\partial z}}\right)_{x}\left({\frac {\partial z}{\partial x}}\right)_{y}=-1.$

• Chain rule (probability):

$\mathrm P(X_1=x_1, \ldots, X_n=x_n) = \prod_{i=1}^n \mathrm P(X_i=x_i \mid X_{i+1}=x_{i+1}, \ldots, X_n=x_n )$

• Chain rule for Kolmogorov complexity:

$K(X,Y) = K(X) + K(Y|X) + O(\log(K(X,Y)))$

• Chain rule for information entropy:

$H(X,Y) = H(X) + H(Y|X)$