The triple product rule, known variously as the cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule, or the reciprocity theorem, is...

scalar triple product and, less often, the vector-valued vector triple product. The scalar triple product (also called the mixed product, box product, or...

Triple product is a ternary operation on vectors. It may also mean: Jacobi triple product, an identity in number theory Triple product rule, a calculus...

Quotient rule – Formula for the derivative of a ratio of functions Triple product rule – Relation between relative derivatives of three variables George...

{\displaystyle z} . The cyclic relation is also known as the cyclic rule or the Triple product rule. Setting the second term in brackets equal to zero yields (...

Multivariable calculus Symmetry of second derivatives Triple product rule, also known as the cyclic chain rule. Cajori, Florian (1952), A History of Mathematical...

above-mentioned triple product expansion (bac–cab rule) can be easily proven using this notation. As mentioned above, the Lie algebra R3 with cross product is isomorphic...

u}}\cdot {\frac {\mathrm {d} u}{\mathrm {d} x}}.} Cyclic chain rule, or triple product rule: ( ∂ x ∂ y ) z ( ∂ y ∂ z ) x ( ∂ z ∂ x ) y = − 1. {\displaystyle...

non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral...

statement of his intent for coordinates that follow the right-hand rule. The cross product of vectors a → {\displaystyle {\vec {a}}} and b → {\displaystyle...

Reciprocity law for Dedekind sums Betti's theorem in linear elasticity The Triple Product rule, a formula relating the partial derivatives of three independent...

under investigation for rule-breaking and violence, were assigned by the State Department to Triple Canopy. Previously, Triple Canopy had been responsible...

{E}{c^{2}}}\mathbf {r} -t\mathbf {p} \right)\right]\end{aligned}}} Using the triple product rule a × ( b × c ) = b ( a ⋅ c ) − c ( a ⋅ b ) ( a × b ) × c = ( c ⋅ a...

rule Kopp's law Noro–Frenkel law of corresponding states Onsager reciprocal relations Stefan number Thermodynamics Timeline of thermodynamics Triple product...

products. In the following, mainly atomic and molecular transitions are considered. In quantum mechanics the basis for a spectroscopic selection rule...

There are two ternary operations involving dot product and cross product. The scalar triple product of three vectors is defined as a ⋅ ( b × c ) = b...

directors consists of Cathy, Richard, and Ross. Richard suggests that their product be some type of food. Cathy has a recipe for apricot jam, so they decide...

Plongeon's and James Churchward's lost continent. Many world religions contain triple deities or concepts of trinity, including the Hindu Trimurti and Tridevi...

test) Trion (physics) Triple-alpha process Triple-resonance nuclear magnetic resonance spectroscopy Triple point Triple product rule Triplet lens Triplet...

^{3})} . The scalar coefficient is the triple product of the three vectors. The cross product and triple product in three dimensions each admit both geometric...

applying the law of the logarithm of a product, the product of the two numbers can be read. More elaborate slide rules can perform other calculations, such...

In organic chemistry, the Cahn–Ingold–Prelog (CIP) sequence rules (also the CIP priority convention; named after Robert Sidney Cahn, Christopher Kelk...

of n-tuples of an m-set is mn. This follows from the combinatorial rule of product. If S is a finite set of cardinality m, this number is the cardinality...

When questioned by the police, Geraldine reveals that her daughter was a product of rape by her uncle, Philip, and she was forced to give up the baby. Then...

R 3 {\displaystyle \mathbb {R} ^{3}} (real-number 3D space) are called triple integrals. For repeated antidifferentiation of a single-variable function...

basic algebraic operations consist of: Also commonly used are the two triple products: Vector calculus studies various differential operators defined on...

 495 BC) starts from an odd number and produces a triple with leg and hypotenuse differing by one unit; the rule attributed to Plato (428/427 or 424/423 – 348/347 BC)...

Double-A Akron RubberDucks. In 48 appearances split between Akron and the Triple-A Columbus Clippers, Kelly pitched to a combined 5–2 record and 2.04 ERA...

for the company; sales of Reese's Pieces tripled, and some retailers had trouble meeting demand for the product. Alongside criticism for trying to ride...

various members mostly Generation X wrestlers, most notably Shawn Michaels, Triple H, Chyna, X-Pac, and the New Age Outlaws, a tag team consisting of Road...