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The reciprocal rule is a special case of the quotient rule in which ... Differentiation of integrals – Problem in mathematics; Differentiation rules – Rules for ...
2.4 Quotient rule for division by a scalar. 2.5 Chain rule. 2.6 Dot product rule. 2.7 Cross product rule. 3 Second derivative identities.
In arithmetic, a quotient (from Latin: quotiens 'how many times', pronounced / ˈ k w oʊ ʃ ən t /) is a quantity produced by the division of two numbers. [1] The quotient has widespread use throughout mathematics.
Division can be calculated with a slide rule by aligning the divisor on the C scale with the dividend on the D scale. The quotient can be found on the D scale where it is aligned with the left index on the C scale. The user is responsible, however, for mentally keeping track of the decimal point.
Derivations of product, quotient, and power rules [ edit ] These are the three main logarithm laws/rules/principles, [ 3 ] from which the other properties listed above can be proven.
The chain rule can be used to derive some well-known differentiation rules. For example, the quotient rule is a consequence of the chain rule and the product rule . To see this, write the function f ( x )/ g ( x ) as the product f ( x ) · 1/ g ( x ) .
This, combined with the sum rule for derivatives, shows that differentiation is linear. The rule for integration by parts is derived from the product rule, as is (a weak version of) the quotient rule. (It is a "weak" version in that it does not prove that the quotient is differentiable but only says what its derivative is if it is differentiable.)
For example, the quotient / = can be conceived of as ... The math we need to know and do in grades preK–5 : concepts, skills, standards, and assessments (2nd ed.).