DOCE DOS Derivadas cociente

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Marlon Arcila

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david arcila was given access to the DOCE DOS 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	Ready to use	Newcastle University Mathematics and Statistics	24/05/2022 12:02
DOCE DOS Derivadas cociente	draft	Marlon Arcila	08/09/2021 00:42
Harry's copy of Differentiation: quotient rule	draft	Harry Flynn	08/05/2018 12:43
Luis's copy of Differentiation: quotient rule	draft	Luis Hernandez	30/11/2018 19:05
Luis's copy of Differentiation: quotient rule	draft	Luis Hernandez	30/11/2018 19:06

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Question statement

Calcular la derivada de la función

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
c	integer	5
b	integer	4
d	integer	-7
s1	integer	-1
d1	integer	-7

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Generated value: `integer`

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"Unnamed part" - prompt
"Unnamed part" → "Unnamed gap" - Correct answer
"Unnamed part" → "Unnamed step" - prompt

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$\simplify[dPoly]{f(x) = ({a} * x + {b}) / Sqrt({c} * x + {d})}$

La derivada tiene la forma:

$\simplify[dPoly]{Diff(f,x,1) = g(x) / (2 * ({c} * x + {d}) ^ (3 / 2))}$

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:

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

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

Ahora sustituimos en la fórmula del cociente:

$\simplify[dPoly]{Diff(f,x,1) = ({a} * Sqrt({c} * x + {d}) -(({a} * x + {b}) * Diff(v,x,1))) / ({c} * x + {d}) = ({a} * Sqrt({c} * x + {d}) -(({c} * ({a} * x + {b})) / (2 * Sqrt({c} * x + {d})))) / ({c} * x + {d}) = ({2 * a} * ({c} * x + {d}) -({c} * ({a} * x + {b}))) / (2 * ({c} * x + {d}) ^ (3 / 2)) = ({a * c} * x + {2 * a * d -(c * b)}) / (2 * ({c} * x + {d}) ^ (3 / 2))}$

Con lo cual se concluye que

$\simplify[dPoly]{g(x) = {a * c} * x + {2 * a * d -(c * b)}}$ .

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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 DOS 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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DOCE DOS Derivadas cociente

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

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

Marlon Arcila 8 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`