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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 () = (), where both f and g are differentiable and () The quotient rule states that the derivative of h(x) is
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.
Let a pair of solution circles be denoted as C A and C B (the pink circles in Figure 6), and let their tangent points with the three given circles be denoted as A 1, A 2, A 3, and B 1, B 2, B 3, respectively. Gergonne's solution aims to locate these six points, and thus solve for the two solution circles.
Power rule; Chain rule; Local linearization; Product rule; Quotient rule; Inverse functions and differentiation; Implicit differentiation; Stationary point. Maxima and minima; First derivative test; Second derivative test; Extreme value theorem; Differential equation; Differential operator; Newton's method; Taylor's theorem; L'Hôpital's rule ...
Special cases of Apollonius' problem are those in which at least one of the given circles is a point or line, i.e., is a circle of zero or infinite radius. The nine types of such limiting cases of Apollonius' problem are to construct the circles tangent to: three points (denoted PPP, generally 1 solution)
In these limits, the infinitesimal change is often denoted or .If () is differentiable at , (+) = ′ ().This is the definition of the derivative.All differentiation rules can also be reframed as rules involving limits.
The owners of a Colorado funeral home accused of piling 190 bodies inside a room-temperature building and giving the grieving relatives fake ashes pleaded guilty Friday to corpse abuse as ...
irrationality of log 2 3; irrationality of the square root of 2; Mathematical induction. sum identity; Power rule. differential of x n; Product and Quotient Rules; Derivation of Product and Quotient rules for differentiating. Prime number. Infinitude of the prime numbers; Primitive recursive function; Principle of bivalence