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differentiable function
función diferenciable

this differentiable quantity is power.
esta cantidad diferencial,es la potencia.

are all continuous functions differentiable?
¿son todas las funciones continuas son diferenciables?

(a) not all continuous functions are differentiable.
(a) no todas las funciones continuas son diferenciables.

(b) however, every differentiable function is continuous.
(b) sin embargo, cada función diferenciable es continua.

its domain is the set of all x at which f is differentiable.
su dominio es el conjunto de toda x a las que existe la derivada f'(x) .

in particular it is possible to use calculus on a differentiable manifold.
en particular, es posible utilizar el cálculo en una variedad diferenciable.

6 let be an increasing differentiable function with and is bounded, and let .
6 let ser cada vez más differentiable función con y limita, y dejar .

find all differentiable functions for which there is a positive real number such that
buscar differentiable funciones para los cuales existe un número real positivo tal que

; sixth remarka differentiable bijection is "not" necessarily a diffeomorphism.
a differentiable bijection is "not" necessarily a diffeomorphism, e.g.

2 function , is continuous on and differentiable on . prove that there exists such that
2 función , es continua en y diferenciable en . demostrar que no existe de tal manera que

, even if a function is continuous at a point, it may not be differentiable there.
por lo tanto, no existe derivada en el punto, a pesar de que sea continuo.

both line searches and trust regions are used in modern methods of non-differentiable optimization.
ambos búsquedas lineales y regiones de confianza son usados en métodos modernos de optimización no diferenciable.

he later extended his methods to study the koch curves which are continuous everywhere but nowhere differentiable.
más tarde amplió sus métodos de estudio de las curvas de koch, que se continua en todas partes pero en ninguna parte diferenciable.

)* (describes a bohmian resolution to the dilemma posed by non-differentiable wavefunctions.
)* (describes a bohmian resolution to the dilemma posed by non-differentiable wavefunctions.

8 the continuous function and twice differentiable function satisfies . prove that there exist two such real numbers and such that .
8 la función continua y dos veces differentiable función satisface . demostrar que existen dos números reales tales y tal que .

(b) there exists a continuously differentiable function such that for each the equation has uncountably many solutions .
(b) existe una función continuamente diferenciable tales que para cada uno la ecuación tiene uncountably muchas soluciones .

for example, if the function is not "infinitely differentiable", one cannot generate a taylor series.
por ejemplo, si la función no es "infinitamente derivable", no se puede generar una serie de taylor.

somewhat surprisingly, a differential equation may have solutions which are not differentiable; and the weak formulation allows one to find such solutions.
sorprendentemente, una ecuación diferencial puede tener soluciones que no son diferenciables; y la formulación débil permite encontrar tales soluciones.

if everything works out fine and the limit exists, then we say that f is differentiable at x. otherwise, we say that f is not differentiable at x.
si todo vaya bien y existe el límite, decimos que f es diferenciable a x. si no, decimos que f no es diferenciable a x.