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