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In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let () = () ...
The reciprocal rule can be derived either from the quotient rule, or from the combination of power rule and chain rule. The quotient rule If f and g are ...
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.)
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.
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).
In that way, it is a weaker result than the reciprocal rule proved above. However, in the context of differential algebra, in which there is nothing that is not differentiable and in which derivatives are not defined by limits, it is in this way that the reciprocal rule and the more general quotient rule are established.
"Try to see the good in people." "Come on − he can't be that bad." "You should be grateful to even be in a relationship.". If you've heard these phrases before, chances are you've been "bright ...
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.