DOCE UNO Derivadas cociente

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Marlon Arcila

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david arcila was given access to the DOCE UNO Derivadas cociente 3 years, 7 months ago

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Marlon Arcila 8 years, 5 months ago

Created this as a copy of Differentiation: Quotient rule.

Name	Status	Author	Last Modified
Differentiation: Quotient rule	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
DOCE UNO Derivadas cociente	draft	Marlon Arcila	08/09/2021 00:42
Luis's copy of Differentiation: Quotient rule	draft	Luis Hernandez	30/11/2018 18:59
diff by quotient rule	draft	Johnny Yi	19/12/2018 01:11

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Question statement

Calcular la derivada de la función

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			Name	Type	Generated Value

a	integer	5
c	integer	4
b	integer	-2
d	integer	6
s2	integer	1
s1	integer	-1
det	integer	38
c1	integer	4

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$\simplify[std]{f(x) = ({a} * x+{b})/({c}x^2+{d})}$
La derivada tiene la forma:

$\frac{df}{dx}=\simplify[std]{g(x)/({c}x^2+{d})^2}$
Cuál es el polinomio

$g(x)$ , con el que la derivada es la correcta

$g(x)=\;$ Unnamed gap

Ejemplo de respuesta: escriba −21x^2−12x+7, si la respuesta es $−21x^2−12x+7$

Advice

Si $u$ y $v$ son funciones derivables de $x$ , entonces se cumple que:

$\simplify[std]{Diff(u/v,x,1) = (v * Diff(u,x,1) - u * Diff(v,x,1))/v^2}$

Para el ejemplo, tenemos que:

$\simplify[std]{u = ({a}x+{b})}\Rightarrow \simplify[std]{Diff(u,x,1) = {a}}$

$\simplify[std]{v = ({c} * x^2+{d})} \Rightarrow \simplify[std]{Diff(v,x,1) = {2*c}x}$

Ahora sustituimos en la fórmula del cociente:

$\begin{eqnarray*} \frac{df}{dx}&=&\simplify[std]{({a}({c}x^2+{d})-{2*c}x({a}x+{b}))/({c}x^2+{d})^2}\\ &=&\simplify[std]{({a*c}x^2+{a*d}-{2*c*a}x^2-{2*c*b}x)/({c}x^2+{d})^2}\\ &=&\simplify[std]{({-c*a}x^2+{-2*b*c}x+{a*d})/({c}x^2+{d})^2} \end{eqnarray*}$

Con lo cual se concluye que $g(x)=\simplify[std]{{-c*a}x^2+{-2*b*c}x+{a*d}}$

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This question is used in the following exams:

6 B Derivada: regla del cociente con raíz by david arcila in WWW Derivadas OK EXAMENES.
18 $y'=f/g$ by david arcila in 2021.

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david arcila was given access to the DOCE UNO Derivadas cociente 3 years, 7 months ago

Marlon Arcila 8 years, 5 months ago

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DOCE UNO Derivadas cociente

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

david arcila was given access to the DOCE UNO Derivadas cociente 3 years, 7 months ago

Marlon Arcila 8 years, 5 months ago

Error in variable testing condition

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Generated value: integer

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Generated value: `integer`