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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 ...
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In calculus, the reciprocal rule gives the derivative of the reciprocal of a function f in terms of the derivative of f. The reciprocal rule can be used to show that the power rule holds for negative exponents if it has already been established for positive exponents.
The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.
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In general, if a binomial factor is raised to the power of , then constants will be needed, each appearing divided by successive powers, (), where runs from 1 to . The cover-up rule can be used to find A n {\displaystyle A_{n}} , but it is still A 1 {\displaystyle A_{1}} that is called the residue .
Big idea: use chain rule to compute rate of change of distance between two vehicles. Plan: Choose coordinate system; Identify variables; Draw picture; Big idea: use chain rule to compute rate of change of distance between two vehicles; Express c in terms of x and y via Pythagorean theorem; Express dc/dt using chain rule in terms of dx/dt and dy/dt
It is unnecessary - an example. It is very bad mathematical writing to clutter up a definition with examples. Put them after the definition. Furthermore "for some real number r" is just rubbish. In the definition r ranges from 0 to n so you are contradicting the definition within itself - bad bad idea.