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Lecture

Integral Calculation

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Chain rule

In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely, if is the function such that for every x, then the chain rule is, in Lagrange's notation, or, equivalently, The chain rule may also be expressed in Leibniz's notation. If a variable z depends on the variable y, which itself depends on the variable x (that is, y and z are dependent variables), then z depends on x as well, via the intermediate variable y.

Zaitsev's rule

In organic chemistry, Zaitsev's rule (or Saytzeff's rule, Saytzev's rule) is an empirical rule for predicting the favored alkene product(s) in elimination reactions. While at the University of Kazan, Russian chemist Alexander Zaitsev studied a variety of different elimination reactions and observed a general trend in the resulting alkenes. Based on this trend, Zaitsev proposed that the alkene formed in greatest amount is that which corresponded to removal of the hydrogen from the alpha-carbon having the fewest hydrogen substituents.

Quotient rule

In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let , where both f and g are differentiable and The quotient rule states that the derivative of h(x) is It is provable in many ways by using other derivative rules. Given , let , then using the quotient rule: The quotient rule can be used to find the derivative of as follows: Reciprocal rule The reciprocal rule is a special case of the quotient rule in which the numerator .

Markovnikov's rule

In organic chemistry, Markovnikov's rule or Markownikoff's rule describes the outcome of some addition reactions. The rule was formulated by Russian chemist Vladimir Markovnikov in 1870. The rule states that with the addition of a protic acid HX or other polar reagent to an asymmetric alkene, the acid hydrogen (H) or electropositive part gets attached to the carbon with more hydrogen substituents, and the halide (X) group or electronegative part gets attached to the carbon with more alkyl substituents.

Related concepts (24)