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The quotient rule states that the derivative of h(x) is ... Differentiation rules – Rules for computing derivatives of functions;
The reciprocal rule can be derived either from the quotient rule, or from the combination of power rule and chain rule. ... Logarithmic differentiation is a technique ...
2.4 Quotient rule for division by a scalar. 2.5 Chain rule. ... Differentiation rules – Rules for computing derivatives of functions; Exterior calculus identities;
[5] [6] The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of length h). [7] [8]: 237 [9] The limit of the difference quotient (i.e., the derivative) is thus the instantaneous rate of change. [9]
The process of finding a derivative is called differentiation. Geometrically, ... These techniques include the chain rule, product rule, and quotient rule.
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.)
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In summary, both derivatives and logarithms have a product rule, a reciprocal rule, a quotient rule, and a power rule (compare the list of logarithmic identities); each pair of rules is related through the logarithmic derivative.