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With hindsight, however, it is considered the first general theorem of calculus to be discovered. [1] The power rule for differentiation was derived by Isaac Newton and Gottfried Wilhelm Leibniz, each independently, for rational power functions in the mid 17th century, who both then used it to derive the power rule for integrals as the inverse ...
The logarithmic derivative is another way of stating the rule for differentiating the logarithm of a function (using the chain rule): () ′ = ′, wherever is positive. Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative.
The antiderivative of − 1 / x 2 can be found with the power rule and is 1 / x ... above formula can ... theorem of calculus to an appropriate product rule.
Pages in category "Theorems in calculus" ... Integration using Euler's formula; ... Power rule; Product rule; Q. Quotient rule; R.
The study of differential calculus is unified with the calculus of finite differences in time scale calculus. [54] The arithmetic derivative involves the function that is defined for the integers by the prime factorization. This is an analogy with the product rule. [55]
The proof of the general Leibniz rule [2]: 68–69 proceeds by induction. Let and be -times differentiable functions.The base case when = claims that: ′ = ′ + ′, which is the usual product rule and is known to be true.