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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 () = () ...
Kissing circles. Given three mutually tangent circles (black), there are, in general, two possible answers (red) as to what radius a fourth tangent circle can have.In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic equation.
I think you're right, but it's been a long time since I took calculus, so hopefully someone else can confirm. Mathworld mentions this rule briefly, but does not mention constraints. Seems to me that g(x) could easily be 0, though. -- Wapcaplet 21:00 18 Jun 2003 (UTC) yes Pizza Puzzle
The validity of this rule follows from the validity of the Feynman method, for one may always substitute a subscripted del and then immediately drop the subscript under the condition of the rule. For example, from the identity A ⋅( B × C ) = ( A × B )⋅ C we may derive A ⋅(∇× C ) = ( A ×∇)⋅ C but not ∇⋅( B × C ) = (∇× B ...
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. It is frequently used to transform the antiderivative of a product of functions into an ...
Also, one can readily deduce the quotient rule from the reciprocal rule and the product rule. The reciprocal rule states that if f is differentiable at a point x and f(x) ≠ 0 then g(x) = 1/f(x) is also differentiable at x and ′ = ′ ().
Gottfried Wilhelm von Leibniz (1646–1716), German philosopher, mathematician, and namesake of this widely used mathematical notation in calculus.. In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols dx and dy to represent infinitely small (or infinitesimal) increments of x and y, respectively ...
The Leibniz rule bears a strong resemblance to the binomial theorem, and in fact the binomial theorem can be proven directly from the Leibniz rule by taking () = and () =, which gives ( a + b ) n e ( a + b ) x = e ( a + b ) x ∑ k = 0 n ( n k ) a n − k b k , {\displaystyle (a+b)^{n}e^{(a+b)x}=e^{(a+b)x}\sum _{k=0}^{n}{\binom {n}{k}}a^{n-k}b ...